Published since January 1, 1826

Journal für die reine und angewandte Mathematik

ISSN: 0075-4102

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

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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Volume 2022 Issue 782

January 2022

Accessible January 1, 2022

Frontmatter

Page range: i-iv

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October 28, 2021

On the torsion values for sections of an elliptic scheme

Pietro Corvaja, Julian Demeio, David Masser, Umberto Zannier

Page range: 1-41

Abstract

We shall consider sections of a complex elliptic scheme ℰ{{{\mathcal{E}}}} over an affine base curve B , and study the points of B where the section takes a torsion value. In particular, we shall relate the distribution in B of these points with the canonical height of the section, proving an integral formula involving a measure on B coming from the so-called Betti map of the section. We shall show that this measure is the same one which appears in dynamical issues related to the section. This analysis will also involve the multiplicity with which a torsion value is attained, which is an independent problem. We shall prove finiteness theorems for the points where the multiplicity is higher than expected. Such multiplicity has also a relation with Diophantine Approximation and quasi-integral points on ℰ{{{\mathcal{E}}}} (over the affine ring of B ), and in Sections 5 and 6 of the paper we shall exploit this viewpoint, proving an effective result in the spirit of Siegel’s theorem on integral points.

October 16, 2021

2-Verma modules

Grégoire Naisse, Pedro Vaz

Page range: 43-108

Abstract

We construct a categorification of parabolic Verma modules for symmetrizable Kac–Moody algebras using KLR-like diagrammatic algebras. We show that our construction arises naturally from a dg-enhancement of the cyclotomic quotients of the KLR-algebras. As a consequence, we are able to recover the usual categorification of integrable modules. We also introduce a notion of dg-2-representation for quantum Kac–Moody algebras, and in particular of parabolic 2-Verma modules.

November 12, 2021

Ellipticity and discrete series

Bernhard Krötz, Job J. Kuit, Eric M. Opdam, Henrik Schlichtkrull

Page range: 109-119

Abstract

We explain by elementary means why the existence of a discrete series representation of a real reductive group G implies the existence of a compact Cartan subgroup of G . The presented approach has the potential to generalize to real spherical spaces.

December 2, 2021

Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups

Sam Shepherd, Daniel J. Woodhouse

Page range: 121-173

Abstract

We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let G be a group that is one-ended, hyperbolic relative to virtually abelian subgroups, and has JSJ decomposition over two-ended subgroups containing only virtually free vertex groups that are not quadratically hanging. Our main result is that any group quasi-isometric to G is abstractly commensurable to G . In particular, our result applies to certain “generic” HNN extensions of a free group over cyclic subgroups.

November 12, 2021

Nonnegative Ricci curvature and escape rate gap

Jiayin Pan

Page range: 175-196

Abstract

Let M be an open n -manifold of nonnegative Ricci curvature and let p∈M{p\in M}. We show that if (M,p){(M,p)} has escape rate less than some positive constant ϵ⁢(n){\epsilon(n)}, that is, minimal representing geodesic loops of π1⁢(M,p){\pi_{1}(M,p)} escape from any bounded balls at a small linear rate with respect to their lengths, then π1⁢(M,p){\pi_{1}(M,p)} is virtually abelian. This generalizes the author’s previous work [J. Pan, On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature, Geom. Topol. 25 2021, 2, 1059–1085], where the zero escape rate is considered.

October 26, 2021

Hyperkähler metrics near Lagrangian submanifolds and symplectic groupoids

Maxence Mayrand

Page range: 197-218

Abstract

The first part of this paper is a generalization of the Feix–Kaledin theorem on the existence of a hyperkähler metric on a neighborhood of the zero section of the cotangent bundle of a Kähler manifold. We show that the problem of constructing a hyperkähler structure on a neighborhood of a complex Lagrangian submanifold in a holomorphic symplectic manifold reduces to the existence of certain deformations of holomorphic symplectic structures. The Feix–Kaledin structure is recovered from the twisted cotangent bundle. We then show that every holomorphic symplectic groupoid over a compact holomorphic Poisson surface of Kähler type has a hyperkähler structure on a neighborhood of its identity section. More generally, we reduce the existence of a hyperkähler structure on a symplectic realization of a holomorphic Poisson manifold of any dimension to the existence of certain deformations of holomorphic Poisson structures adapted from Hitchin’s unobstructedness theorem.

Open Access November 12, 2021

On the geometry of lattices and finiteness of Picard groups

Florian Eisele

Page range: 219-233

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Abstract

Let (K,𝒪,k){(K,\mathcal{O},k)} be a p -modular system with k algebraically closed and 𝒪{\mathcal{O}} unramified, and let Λ be an 𝒪{\mathcal{O}}-order in a separable K -algebra. We call a Λ-lattice L rigid if ExtΛ1⁡(L,L)=0{{\operatorname{Ext}}^{1}_{\Lambda}(L,L)=0}, in analogy with the definition of rigid modules over a finite-dimensional algebra. By partitioning the Λ-lattices of a given dimension into “varieties of lattices”, we show that there are only finitely many rigid Λ-lattices L of any given dimension. As a consequence we show that if the first Hochschild cohomology of Λ vanishes, then the Picard group and the outer automorphism group of Λ are finite. In particular, the Picard groups of blocks of finite groups defined over 𝒪{\mathcal{O}} are always finite.

October 26, 2021

About every convex set in any generic Riemannian manifold

Alexander Lytchak, Anton Petrunin

Page range: 235-245

Abstract

We give a necessary condition on a geodesic in a Riemannian manifold that can run in some convex hypersurface. As a corollary, we obtain peculiar properties that hold true for every convex set in any generic Riemannian manifold (M,g){(M,g)}. For example, if a convex set in (M,g){(M,g)} is bounded by a smooth hypersurface, then it is strictly convex.

October 28, 2021

Hopf-type theorem for self-shrinkers

Hilário Alencar, Gregório Silva Neto, Detang Zhou

Page range: 247-279

Abstract

In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three-dimensional Euclidean space ℝ3{{\mathbb{R}}^{3}} is a round sphere, provided its mean curvature and the norm of the its position vector have an upper bound in terms of the norm of its traceless second fundamental form. The example constructed by Drugan justifies that the hypothesis on the second fundamental form is necessary. We can also prove the same kind of rigidity results for surfaces with parallel weighted mean curvature vector in ℝn{{\mathbb{R}}^{n}} with radial weight. These results are applications of a new generalization of Cauchy’s Theorem in complex analysis which concludes that a complex function is identically zero or its zeroes are isolated if it satisfies some weak holomorphy.

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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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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
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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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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; 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

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: 0075-4102
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