Published since January 1, 1826

Journal für die reine und angewandte Mathematik

ISSN: 1435-5345

Edited by: Tobias Colding, Ana Caraiani, Jun-Muk Hwang, Olivier Schiffmann, Jakob Stix, Gábor Székelyhidi

Managing Editor: Daniel Huybrechts

Impact Factor: 1.809

About this journal

August Leopold Crelle (1780 - 1855)

The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of "Crelle's Journal". In the 190 years of its existence, "Crelle's Journal" has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI's Journal Citation Report.

Abstracting and Indexing

Journal für die reine und angewandte Mathematik is covered by the following services:

Baidu Scholar
Cabells Journalytics
CNKI Scholar (China National Knowledge Infrastructure)
CNPIEC - cnpLINKer
Dimensions
EBSCO (relevant databases)
EBSCO Discovery Service
Genamics JournalSeek
Google Scholar
Japan Science and Technology Agency (JST)
J-Gate
Journal Citation Reports/Science Edition
JournalGuide
JournalTOCs
KESLI-NDSL (Korean National Discovery for Science Leaders)
Mathematical Reviews (MathSciNet)
MyScienceWork
Naver Academic
Naviga (Softweco)
Primo Central (ExLibris)
ProQuest (relevant databases)
Publons
QOAM (Quality Open Access Market)
ReadCube
SCImago (SJR)
SCOPUS
Semantic Scholar
Sherpa/RoMEO
Summon (ProQuest)
TDNet
Ulrich's Periodicals Directory/ulrichsweb
WanFang Data
Web of Science - Current Contents/Physical, Chemical and Earth Sciences
Web of Science - Science Citation Index
Web of Science - Science Citation Index Expanded
WorldCat (OCLC)
X-MOL
Yewno Discover
zbMATH Open

Supplementary Materials

Topics

Volume 2023 Issue 795

February 2023

Publicly Available February 1, 2023

Frontmatter

Page range: i-iv

Download PDF

Open Access December 6, 2022

Squarefrees are Gaussian in short intervals

Ofir Gorodetsky, Alexander Mangerel, Brad Rodgers

Page range: 1-44

More Download PDF

Abstract

We show that counts of squarefree integers up to X in short intervals of size H tend to a Gaussian distribution as long as H → ∞ {H\to\infty} and H = X o ⁢ ( 1 ) {H=X^{o(1)}} . This answers a question posed by R. R. Hall in 1989. More generally, we prove a variant of Donsker’s theorem, showing that these counts scale to a fractional Brownian motion with Hurst parameter 1 / 4 {1/4} . In fact, we are able to prove these results hold in general for collections of B -free integers as long as the sieving set B satisfies a very mild regularity property, for Hurst parameter varying with the set B .

Open Access December 6, 2022

Effective generation for foliated surfaces: Results and applications

Calum Spicer, Roberto Svaldi

Page range: 45-84

More Download PDF

Abstract

We explore the birational structure and invariants of a foliated surface ( X , F ) (X,\mathcal{F}) in terms of the adjoint divisor K F + ϵ ⁢ K X K_{\mathcal{F}}+\epsilon K_{X} , 0 < ϵ ≪ 1 0<\epsilon\ll 1 . We then establish a bound on the automorphism group of an adjoint general type foliated surface ( X , F ) (X,\mathcal{F}) , provide a bound on the degree of a general curve invariant by an algebraically integrable foliation on a surface and prove that the set of 𝜖-adjoint canonical models of foliations of general type and with fixed volume form a bounded family.

November 23, 2022

Uniqueness of compact ancient solutions to the higher-dimensional Ricci flow

Simon Brendle, Panagiota Daskalopoulos, Keaton Naff, Natasa Sesum

Page range: 85-138

Abstract

In dimensions n ≥ 4 {n\geq 4} , an ancient κ-solution is a nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is κ-noncollapsed. In this paper, we study the classification of ancient κ-solutions to n -dimensional Ricci flow on S n {S^{n}} , extending the result in [S. Brendle, P. Daskalopoulos and N. Sesum, Uniqueness of compact ancient solutions to three-dimensional Ricci flow, Invent. Math. 226 2021, 2, 579–651] to higher dimensions. We prove that such a solution is either isometric to a family of shrinking round spheres, or the Type II ancient solution constructed by Perelman.

December 1, 2022

Shuffle algebras for quivers and wheel conditions

Andrei Neguţ

Page range: 139-182

Abstract

We show that the shuffle algebra associated to a doubled quiver (determined by 3-variable wheel conditions) is generated by elements of minimal degree. Together with results of Varagnolo–Vasserot and Yu Zhao, this implies that the aforementioned shuffle algebra is isomorphic to the localized 𝐾-theoretic Hall algebra associated to the quiver by Grojnowski, Schiffmann–Vasserot and Yang–Zhao. With small modifications, our theorems also hold under certain specializations of the equivariant parameters, which will allow us in joint work with Sala and Schiffmann to give a generators-and-relations description of the Hall algebra of any curve over a finite field (which is a shuffle algebra due to Kapranov–Schiffmann–Vasserot). When the quiver has no edge loops or multiple edges, we show that the shuffle algebra, localized 𝐾-theoretic Hall algebra, and the positive half of the corresponding quantum loop group are all isomorphic; we also obtain the non-degeneracy of the Hopf pairing on the latter quantum loop group.

December 16, 2022

Variation of canonical height for\break Fatou points on ℙ¹

Laura DeMarco, Niki Myrto Mavraki

Page range: 183-220

Abstract

Let f : ℙ 1 → ℙ 1 {f:\mathbb{P}^{1}\to\mathbb{P}^{1}} be a map of degree > 1 {>1} defined over a function field k = K ⁢ ( X ) {k=K(X)} , where K is a number field and X is a projective curve over K . For each point a ∈ ℙ 1 ⁢ ( k ) {a\in\mathbb{P}^{1}(k)} satisfying a dynamical stability condition, we prove that the Call–Silverman canonical height for specialization f t {f_{t}} at point a t {a_{t}} , for t ∈ X ⁢ ( ℚ ¯ ) {t\in X(\overline{\mathbb{Q}})} outside a finite set, induces a Weil height on the curve X ; i.e., we prove the existence of a ℚ {\mathbb{Q}} -divisor D = D f , a {D=D_{f,a}} on X so that the function t ↦ h ^ f t ⁢ ( a t ) - h D ⁢ ( t ) {t\mapsto\hat{h}_{f_{t}}(a_{t})-h_{D}(t)} is bounded on X ⁢ ( ℚ ¯ ) {X(\overline{\mathbb{Q}})} for any choice of Weil height associated to D . We also prove a local version, that the local canonical heights t ↦ λ ^ f t , v ⁢ ( a t ) {t\mapsto\hat{\lambda}_{f_{t},v}(a_{t})} differ from a Weil function for D by a continuous function on X ⁢ ( ℂ v ) {X(\mathbb{C}_{v})} , at each place v of the number field K . These results were known for polynomial maps f and all points a ∈ ℙ 1 ⁢ ( k ) {a\in\mathbb{P}^{1}(k)} without the stability hypothesis, [21, 14], and for maps f that are quotients of endomorphisms of elliptic curves E over k and all points a ∈ ℙ 1 ⁢ ( k ) {a\in\mathbb{P}^{1}(k)} . [32, 29]. Finally, we characterize our stability condition in terms of the geometry of the induced map f ~ : X × ℙ 1 ⇢ X × ℙ 1 {\tilde{f}:X\times\mathbb{P}^{1}\dashrightarrow X\times\mathbb{P}^{1}} over K ; and we prove the existence of relative Néron models for the pair ( f , a ) {(f,a)} , when a is a Fatou point at a place γ of k , where the local canonical height λ ^ f , γ ⁢ ( a ) {\hat{\lambda}_{f,\gamma}(a)} can be computed as an intersection number.

December 15, 2022

Failure of strong unique continuation for harmonic functions on RCD spaces

Qin Deng, Xinrui Zhao

Page range: 221-241

Abstract

Unique continuation of harmonic functions on RCD {\operatorname{RCD}} space is a long-standing open problem, with little known even in the setting of Alexandrov spaces. In this paper, we establish the weak unique continuation theorem for harmonic functions on RCD ⁡ ( K , 2 ) {\operatorname{RCD}(K,2)} spaces and give a counterexample for strong unique continuation in the setting of RCD ⁡ ( K , N ) {\operatorname{RCD}(K,N)} space for any N ≥ 4 {N\geq 4} and any K ∈ ℝ {K\in\mathbb{R}} .

January 27, 2023

The relative Bogomolov conjecture for fibered products of elliptic curves

Lars Kühne

Page range: 243-270

Abstract

We deduce an analogue of the Bogomolov conjecture for non-degenerate subvarieties in fibered products of families of elliptic curves from the author’s recent theorem on equidistribution in families of abelian varieties. This generalizes results of DeMarco and Mavraki and improves certain results of Manin–Mumford type proven by Masser and Zannier to results of Bogomolov type, yielding the first results of this type for subvarieties of relative dimension > 1 {>1} in families of abelian varieties with trivial trace.

January 27, 2023

q-opers, QQ-systems, and Bethe Ansatz II: Generalized minors

Peter Koroteev, Anton M. Zeitlin

Page range: 271-296

Abstract

In this paper, we describe a certain kind of q -connections on a projective line, namely Z -twisted ( G , q ) {(G,q)} -opers with regular singularities using the language of generalized minors. In part one we explored the correspondence between these q -connections and 𝑄𝑄 \mathit{QQ} -systems/Bethe Ansatz equations. Here we associate to a Z -twisted ( G , q ) {(G,q)} -oper a class of meromorphic sections of a G -bundle, satisfying certain difference equations, which we refer to as ( G , q ) {(G,q)} -Wronskians. Among other things, we show that the 𝑄𝑄 \mathit{QQ} -systems and their extensions emerge as the relations between generalized minors, thereby putting the Bethe Ansatz equations in the framework of cluster mutations known in the theory of double Bruhat cells.

Ahead of Print / Just Accepted

Ahead of Print / Just Accepted

Volume 2023

Volume 2022

Volume 2021

Volume 2020

Volume 2019

Volume 2018

Volume 2017

Volume 2016

Volume 2015

Volume 2014

Volume 2013

Volume 2012

Volume 2011

Volume 2010

Volume 2009

Volume 2008

Volume 2007

Volume 2006

Volume 2005

Volume 2004

Volume 2003

Volume 2002

Volume 2001

Volume 2000

Volume 1999

Volume 1998

Volume 1997

Volume 1996

Volume 1995

Volume 1994

Volume 1993

Volume 1992

Volume 1991

Volume 1990

Volume 1989

Volume 1988

Volume 1987

Volume 1986

Volume 1985

Volume 1984

Volume 1983

Volume 1982

Volume 1981

Volume 1980

Volume 1979

Volume 1978

Volume 1977

Volume 1976

Volume 1975

Volume 1974

Volume 1973

Volume 1972

Volume 1971

Volume 1970

Volume 1969

Volume 1968

Volume 1967

Volume 1966

Volume 1965

Volume 1964

Volume 1963

Issue 212

Volume 1962

Volume 1961

Volume 1960

Volume 1959

Volume 1958

Volume 1957

Volume 1956

Issue 196

Volume 1955

Volume 1954

Issue 193

Volume 1953

Volume 1952

Issue 190

Volume 1951

Issue 189

Volume 1950

Volume 1940

Volume 1939

Issue 180

Volume 1938

Volume 1937

Volume 1936

Volume 1935

Volume 1934

Volume 1933

Issue 169

Volume 1932

Volume 1931

Volume 1930

Volume 1929

Volume 1928

Issue 159

Volume 1927

Volume 1926

Issue 155

Volume 1925

Issue 154

Volume 1924

Issue 153

Volume 1923

Issue 152

Volume 1921

Issue 151

Volume 1920

Issue 150

Volume 1919

Issue 149

Volume 1918

Issue 148

Volume 1917

Issue 147

Volume 1916

Issue 146

Volume 1915

Issue 145

Volume 1914

Issue 144

Volume 1913

Volume 1912

Issue 141

Volume 1911

Volume 1910

Volume 1909

Volume 1908

Volume 1907

Issue 132

Volume 1906

Issue 131

Volume 1905

Volume 1904

Issue 127

Volume 1903

Volume 1902

Issue 124

Volume 1901

Issue 123

Volume 1900

Volume 1899

Issue 120

Volume 1898

Issue 119

Volume 1897

Volume 1896

Issue 116

Volume 1895

Volume 1894

Issue 113

Volume 1893

Volume 1892

Volume 1891

Volume 1890

Issue 106

Volume 1889

Volume 1888

Volume 1887

Volume 1886

Issue 99

Volume 1885

Issue 98

Volume 1884

Volume 1883

Volume 1882

Volume 1881

Volume 1880

Volume 1879

Volume 1878

Volume 1877

Volume 1876

Issue 81

Volume 1875

Volume 1874

Volume 1873

Volume 1872

Issue 74

Volume 1871

Issue 73

Volume 1870

Volume 1869

Issue 70

Volume 1868

Volume 1867

Issue 67

Volume 1866

Volume 1865

Issue 64

Volume 1864

Issue 63

Volume 1863

Volume 1862

Issue 60

Volume 1861

Volume 1860

Issue 57

Volume 1859

Issue 56

Volume 1858

Issue 55

Volume 1857

Volume 1856

Volume 1855

Volume 1854

Volume 1853

Volume 1852

Volume 1851

Volume 1850

Volume 1849

Issue 38

Volume 1848

Volume 1847

Volume 1846

Volume 1845

Issue 29

Volume 1844

Volume 1843

Volume 1842

Volume 1841

Issue 22

Volume 1840

Volume 1839

Issue 19

Volume 1838

Issue 18

Volume 1837

Volume 1836

Issue 15

Volume 1835

Volume 1834

Volume 1833

Issue 10

Volume 1832

Volume 1831

Issue 7

Volume 1830

Volume 1829

Issue 4

Volume 1828

Issue 3

Volume 1827

Issue 2

Volume 1826

Issue 1

5-year Impact Factor	1.868
Cite Score	3.1
Impact Factor	1.809
Journal Citation Indicator	1.92
Mathematical Citation Quotient	1.44
SCImago Journal Rank	2.424
Source Normalized Impact per Paper	1.916

Submit

Submission
Manuscripts should be submitted in electronic form to the editor most closely associated with the topic discussed, in case of doubt to the Managing Editor. Names and addresses of the editors (including e-mail addresses) are given in the Editorial Information.

To facilitate the publication process, authors are encouraged to submit the final manuscript typed using plain TEX or one of its derivatives. Please download the class file here. In doubt please consult the editor concerning details before sending an electronic manuscript.

Your benefits of publishing with us

Fast access to articles due to ahead of print publishing
High Impact Factor
Mathematical Citation Quotient
Every article easily discoverable because of Search Engine Optimization (SEO) and comprehensive abstracting and indexing services
Convenient citation tracking vie e-mail alert
Secure archiving by De Gruyter and the independent archiving service Portico
Professional sales and marketing activities

Submission process
Set your manuscript according to the guidelines below

Each paper should include a short but informative abstract, as well as the Mathematics Subject Classification 2010 representing the primary and secondary subjects of the article
Crelle's Journal follows the traditional style of presentation and layout that has been part of this journal since its inception. This applies to formulas, references and other. Our copyediting will help you with adapting your accepted manuscripts to the Crelle style
In the title formulas or mathematical symbols should be avoided, if possible, or kept to a minimum. Only the first word and proper nouns should be capitalized. If the title is long, a shortened version should be supplied for the running heads, which together with the author’s name should not exceed 80 characters
Proclamations such as Proposition, Theorem, Lemma, Corollary are set in boldface, followed by the text in italics. Numerals in mathematical expressions should always be Roman
Proclamations such as Remark, Definition, Example are set in boldface, but followed by the text in Roman (not italic) typeface
Numbering of displayed formulas is flush left
Footnotes should be numbered consecutively and placed at the foot of the page to which they refer
References should be listed alphabetically and conform to the following example:
[3] H. Hasse, Symmetrische Matrizen im Körper der reellen Zahlen, J. reine angew. Math. 153 (1923), 12–43.
Authors’ addresses should appear at the end of the manuscript, following the list of references. An e-mail address should be included if available
Submit the article in electronic form to the editor most closely associated with the topic discussed, in case of doubt to the Managing Editor. Names and addresses of the editors (including e-mail addresses) are given in the Editorial Information

Please note

Manuscripts of articles should be in English, French or German. Authors whose native language is not English, French or German are asked to have their article carefully checked by a native speaker
Before submitting a paper please get familiar with our Publication Ethics and Malpractice Statement as well as Copyright Agreement
Once your article is accepted you have the option to publish it
Our repository policy allows you to distribute 30 PDF copies of your published article to colleagues (the PDF has to include the information that it is an author's copy). Please also feel free to distribute the link to the online abstract
If you have any general questions please visit our FAQ page for authors

We look forward to receiving your manuscript!

Hybrid Open Access

In this journal, authors have the option to publish their article under an open access license. Open Access allows you as an author to retain copyright and share your findings with colleagues and interested parties worldwide without any restraints.
Please note that authors from institutions with which we have a transformative agreement can publish open access without paying an article processing charge (APC). More information on the eligible institutions and articles can be found under the "Funding and Support" tab here.

Editorial

Editors

Tobias H. Colding; Department of Mathematics, Massachusetts Institute of Technology; 77 Massachusetts Avenue, Cambridge, MA 02139-4307; USA; email: journals@math.mit.edu

Ana Caraiani; Mathematisches Institut, Universität Bonn; Endenicher Allee 60, 53115 Bonn; Germany; email: caraiani@math.uni-bonn.de

Daniel Huybrechts; Mathematisches Institut, Universität Bonn; Endenicher Allee 60, 53115 Bonn; Germany; email: huybrech@math.uni-bonn.de

Jun-Muk Hwang; Institute for Basic Science, Center for Complex Geometry, Daejeon, Korea (South); email: jmhwang@ibs.re.kr

Olivier Schiffmann; Institut de Mathématiques d’Orsay, Faculté des Sciences d’Orsay, Bat. 307, 91405 Orsay Cedex, France; email: olivier.schiffmann@cnrs.fr

Jakob Stix; Institut für Mathematik, Johann Wolfgang Goethe-Universität, Robert-Mayer-Str. 6-8, 60325 Frankfurt am Main, Germany; email: stix.crelle@math.uni-frankfurt.de

Gábor Székelyhidi; Mathematics Department, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208; USA; email: gaborsz@northwestern.edu

Managing Editor

Daniel Huybrechts; Mathematisches Institut, Universität Bonn; Endenicher Allee 60, 53115 Bonn; Germany; email: crelle@math.uni-bonn.de

(Deutsch)

Online ISSN: 1435-5345
Print ISSN: 0075-4102
Type: Journal
Languages: English, German, French
Publisher: De Gruyter
First published: January 1, 1826
Publication Frequency: 12 Issues per Year
Audience: Researchers interested in pure and applied mathematics

Journal für die reine und angewandte Mathematik

Frontmatter

Squarefrees are Gaussian in short intervals

Abstract

Effective generation for foliated surfaces: Results and applications

Abstract

Uniqueness of compact ancient solutions to the higher-dimensional Ricci flow

Abstract

Shuffle algebras for quivers and wheel conditions

Abstract

Variation of canonical height for\break Fatou points on ℙ1

Abstract

Failure of strong unique continuation for harmonic functions on RCD spaces

Abstract

The relative Bogomolov conjecture for fibered products of elliptic curves

Abstract

q-opers, QQ-systems, and Bethe Ansatz II: Generalized minors

Abstract

Variation of canonical height for\break Fatou points on ℙ¹