Published since January 1, 1826

Journal für die reine und angewandte Mathematik

ISSN: 1435-5345

Edited by: Tobias Colding, Daniel Huybrechts, Jun-Muk Hwang, Jakob Stix, Geordie Williamson

Managing Editor: Rainer Weissauer

Impact Factor: 1.713

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.

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Supplementary Materials

Topics

Volume 2021 Issue 779

October 2021

Accessible October 1, 2021

Frontmatter

Page range: i-iv

Download PDF

July 1, 2021

Variation of singular Kähler–Einstein metrics: Positive Kodaira dimension

Junyan Cao, Henri Guenancia, Mihai Păun

Page range: 1-36

Abstract

Given a Kähler fiber space p:X→Y{p:X\to Y} whose generic fiber is of general type, we prove that the fiberwise singular Kähler–Einstein metric induces a semipositively curved metric on the relative canonical bundle KX/Y{K_{X/Y}} of p . We also propose a conjectural generalization of this result for relative twisted Kähler–Einstein metrics. Then we show that our conjecture holds true if the Lelong numbers of the twisting current are zero. Finally, we explain the relevance of our conjecture for the study of fiberwise Song–Tian metrics (which represent the analogue of KE metrics for fiber spaces whose generic fiber has positive but not necessarily maximal Kodaira dimension).

August 14, 2021

On the rotational symmetry of 3-dimensional κ-solutions

Richard H. Bamler, Bruce Kleiner

Page range: 37-55

Abstract

In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional κ-solutions. In this paper, we present an alternative proof for this fact and show that compact κ-solutions are rotationally symmetric. Our proof arose from independent work relating to our Strong Stability Theorem for singular Ricci flows.

July 1, 2021

Automorphic ℒ‐invariants for reductive groups

Lennart Gehrmann

Page range: 57-103

Abstract

Let G be a reductive group over a number field F , which is split at a finite place 𝔭{\mathfrak{p}} of F , and let π be a cuspidal automorphic representation of G , which is cohomological with respect to the trivial coefficient system and Steinberg at 𝔭{\mathfrak{p}}. We use the cohomology of 𝔭{\mathfrak{p}}-arithmetic subgroups of G to attach automorphic ℒ{\mathcal{L}}-invariants to π. This generalizes a construction of Darmon (respectively Spieß), who considered the case G=GL2{G={\mathrm{GL}}_{2}} over the rationals (respectively over a totally real number field). These ℒ{\mathcal{L}}-invariants depend a priori on a choice of degree of cohomology, in which the representation π occurs. We show that they are independent of this choice provided that the π-isotypic part of cohomology is cyclic over Venkatesh’s derived Hecke algebra. Further, we show that automorphic ℒ{\mathcal{L}}-invariants can be detected by completed cohomology. Combined with a local-global compatibility result of Ding it follows that for certain representations of definite unitary groups the automorphic ℒ{\mathcal{L}}-invariants are equal to the Fontaine–Mazur ℒ{\mathcal{L}}-invariants of the associated Galois representation.

August 14, 2021

A p-adic variant of Kontsevich–Zagier integral operation rules and of Hrushovski–Kazhdan style motivic integration

Raf Cluckers, Immanuel Halupczok

Page range: 105-121

Abstract

We prove that if two semi-algebraic subsets of ℚpn{\mathbb{Q}_{p}^{n}} have the same p -adic measure, then this equality can already be deduced using only some basic integral transformation rules. On the one hand, this can be considered as a positive answer to a p -adic analogue of a question asked by Kontsevich–Zagier in the reals (though the question in the reals is much harder). On the other hand, our result can also be considered as stating that over ℚp{\mathbb{Q}_{p}}, universal motivic integration (in the sense of Hrushovski–Kazhdan) coincides with the usual p -adic integration.

July 1, 2021

Harmonic branched coverings and uniformization of CAT(k) spheres

Christine Breiner, Chikako Mese

Page range: 123-166

Abstract

Let S be a surface with a metric d satisfying an upper curvature bound in the sense of Alexandrov (i.e. via triangle comparison). We show that an almost conformal harmonic map from a surface into (S,d){(S,d)} is a branched covering. As a consequence, if (S,d){(S,d)} is homeomorphically equivalent to the 2-sphere 𝕊2{\mathbb{S}^{2}}, then it is conformally equivalent to 𝕊2{\mathbb{S}^{2}}.

August 14, 2021

Bounding non-rationality of divisors on 3-fold Fano fibrations

Caucher Birkar, Konstantin Loginov

Page range: 167-188

Abstract

In this paper we investigate non-rationality of divisors on 3-fold log Fano fibrations (X,B)→Z{(X,B)\to Z} under mild conditions. We show that if D is a component of B with coefficient ≥t>0{\geq t>0} which is contracted to a point on Z , then D is birational to ℙ1×C{\mathbb{P}^{1}\times C}, where C is a smooth projective curve with gonality bounded depending only on t . Moreover, if t>12{t>\frac{1}{2}}, then genus of C is bounded depending only on t .

August 17, 2021

Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces

José Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Alberto Rodríguez-Vázquez

Page range: 189-222

Abstract

We conclude the classification of cohomogeneity one actions on symmetric spaces of rank one by classifying cohomogeneity one actions on quaternionic hyperbolic spaces up to orbit equivalence. As a by-product of our proof, we produce uncountably many examples of inhomogeneous isoparametric families of hypersurfaces with constant principal curvatures in quaternionic hyperbolic spaces.

August 14, 2021

Milnor excision for motivic spectra

Elden Elmanto, Marc Hoyois, Ryomei Iwasa, Shane Kelly

Page range: 223-235

Abstract

We prove that the ∞{\infty}-category of motivic spectra satisfies Milnor excision: if A→B{A\to B} is a morphism of commutative rings sending an ideal I⊂A{I\subset A} isomorphically onto an ideal of B , then a motivic spectrum over A is equivalent to a pair of motivic spectra over B and A/I{A/I} that are identified over B/I⁢B{B/IB}. Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We also prove Milnor excision for Ayoub’s étale motives over schemes of finite virtual cohomological dimension.

Ahead of Print / Just Accepted

Ahead of Print / Just Accepted

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5-year Impact Factor	1.740
Cite Score	3.2
Impact Factor	1.713
Journal Citation Indicator	2.20
Mathematical Citation Quotient	1.44
SCImago Journal Rank	2.562
Source Normalized Impact per Paper	1.625

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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
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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
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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

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Editorial

Editors

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

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

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

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

Geordie Williamson; School of Mathematics and Statistics F07, University of Sydney, Sydney, NSW 2006, Australia; e-mail: williamsoncrelle@gmail.com

Managing Editor

Rainer Weissauer; Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg; Im Neuenheimer Feld 288, 69120 Heidelberg; Germany; Phone: +49 (0)6221 54-5692; Fax: +49 (0)6221 54-8312; e-mail: weissauer.crelle@mathi.uni-heidelberg.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