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 778

September 2021

Accessible September 1, 2021

Frontmatter

Page range: i-iv

Download PDF

July 1, 2021

Non-archimedean hyperbolicity and applications

Ariyan Javanpeykar, Alberto Vezzani

Page range: 1-29

Abstract

Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field K of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is K -analytically Brody hyperbolic in equal characteristic 0. These two results are predicted by the Green–Griffiths–Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use Scholze’s uniformization theorem to prove that the aforementioned moduli space satisfies a non-archimedean analogue of the “Theorem of the Fixed Part” in mixed characteristic.

Open Access July 1, 2021

Deligne–Lusztig duality on the stack of local systems

Dario Beraldo

Page range: 31-63

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Abstract

In the setting of the geometric Langlands conjecture, we argue that the phenomenon of divergence at infinity on BunG{\operatorname{Bun}_{G}} (that is, the difference between !{!}-extensions and *{*}-extensions) is controlled, Langlands-dually, by the locus of semisimple Gˇ{{\check{G}}}-local systems. To see this, we first rephrase the question in terms of Deligne–Lusztig duality and then study the Deligne–Lusztig functor 𝖣𝖫Gspec{\mathsf{DL}_{G}^{\mathrm{spec}}} acting on the spectral Langlands DG category IndCoh𝒩⁢(LSG){{\mathrm{IndCoh}}_{\mathcal{N}}({\mathrm{LS}}_{G})}. We prove that 𝖣𝖫Gspec{\mathsf{DL}_{G}^{\mathrm{spec}}} is the projection IndCoh𝒩⁢(LSG)↠QCoh⁢(LSG){{\mathrm{IndCoh}}_{\mathcal{N}}({\mathrm{LS}}_{G})\twoheadrightarrow{\mathrm{% QCoh}}({\mathrm{LS}}_{G})}, followed by the action of a coherent D -module StG∈𝔇⁢(LSG){{\mathrm{St}}_{G}\in\mathfrak{D}({\mathrm{LS}}_{G})}, which we call the Steinberg D -module. We argue that StG{{\mathrm{St}}_{G}} might be regarded as the dualizing sheaf of the locus of semisimple G -local systems. We also show that 𝖣𝖫Gspec{\mathsf{DL}_{G}^{\mathrm{spec}}}, while far from being conservative, is fully faithful on the subcategory of compact objects.

April 19, 2021

Motivic decompositions for the Hilbert scheme of points of a K3 surface

Andrei Neguţ, Georg Oberdieck, Qizheng Yin

Page range: 65-95

Abstract

We construct an explicit, multiplicative Chow–Künneth decomposition for the Hilbert scheme of points of a K3 surface. We further refine this decomposition with respect to the action of the Looijenga–Lunts–Verbitsky Lie algebra.

June 10, 2021

Extending meromorphic connections to coadmissible ̑𝒟-modules

Thomas Bitoun, Andreas Bode

Page range: 97-118

Abstract

We investigate when a meromorphic connection on a smooth rigid analytic variety 𝑋 gives rise to a coadmissible D⏜X\overparen{\mathcal{D}}_{X}-module, and show that this is always the case when the roots of the corresponding 𝑏-functions are all of positive type. We also use this theory to give an example of an integrable connection on the punctured unit disk whose pushforward is not a coadmissible module.

May 29, 2021

Brauer’s Height Zero Conjecture for principal blocks

Gunter Malle, Gabriel Navarro

Page range: 119-125

Abstract

We prove the other half of Brauer’s Height Zero Conjecture in the case of principal blocks.

June 1, 2021

Four-dimensional complete gradient shrinking Ricci solitons

Huai-Dong Cao, Ernani Ribeiro Jr, Detang Zhou

Page range: 127-144

Abstract

In this article, we study four-dimensional complete gradient shrinking Ricci solitons. We prove that a four-dimensional complete gradient shrinking Ricci soliton satisfying a pointwise condition involving either the self-dual or anti-self-dual part of the Weyl tensor is either Einstein, or a finite quotient of either the Gaussian shrinking soliton ℝ4{\mathbb{R}^{4}}, or 𝕊3×ℝ{\mathbb{S}^{3}\times\mathbb{R}}, or 𝕊2×ℝ2.{\mathbb{S}^{2}\times\mathbb{R}^{2}.} In addition, we provide some curvature estimates for four-dimensional complete gradient Ricci solitons assuming that its scalar curvature is suitable bounded by the potential function.

May 29, 2021

Siegel domains over Finsler symmetric cones

Cho-Ho Chu

Page range: 145-169

Abstract

Let Ω be a proper open cone in a real Banach space V . We show that the tube domain V⊕i⁢Ω{V\oplus i\Omega} over Ω is biholomorphic to a bounded symmetric domain if and only if Ω is a normal linearly homogeneous Finsler symmetric cone, which is equivalent to the condition that V is a unital JB-algebra in an equivalent norm and Ω is the interior of {v2:v∈V}{\{v^{2}:v\in V\}}.

April 29, 2021

Basis divisors and balanced metrics

Yanir A. Rubinstein, Gang Tian, Kewei Zhang

Page range: 171-218

Abstract

Using log canonical thresholds and basis divisors Fujita–Odaka introduced purely algebro-geometric invariants δm{\delta_{m}} whose limit in m is now known to characterize uniform K-stability on a Fano variety. As shown by Blum–Jonsson this carries over to a general polarization, and together with work of Berman, Boucksom, and Jonsson, it is now known that the limit of these δm{\delta_{m}}-invariants characterizes uniform Ding stability. A basic question since Fujita–Odaka’s work has been to find an analytic interpretation of these invariants. We show that each δm{\delta_{m}} is the coercivity threshold of a quantized Ding functional on the m th Bergman space and thus characterizes the existence of balanced metrics. This approach has a number of applications. The most basic one is that it provides an alternative way to compute these invariants, which is new even for ℙn{{\mathbb{P}}^{n}}. Second, it allows us to introduce algebraically defined invariants that characterize the existence of Kähler–Ricci solitons (and the more general g -solitons of Berman–Witt Nyström), as well as coupled versions thereof. Third, it leads to approximation results involving balanced metrics in the presence of automorphisms that extend some results of Donaldson.

Accessible July 1, 2021

Erratum to The braided Thompson's groups are of type F_∞ (J. reine angew. Math. 718 (2016), 59–101)

Kai-Uwe Bux, Stefan Witzel, Matthew C. B. Zaremsky

Page range: 219-221

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Cite Score	3.2
Impact Factor	1.713
Journal Citation Indicator	2.20
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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
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[3] H. Hasse, Symmetrische Matrizen im Körper der reellen Zahlen, J. reine angew. Math. 153 (1923), 12–43.
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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

Journal für die reine und angewandte Mathematik

Frontmatter

Non-archimedean hyperbolicity and applications

Abstract

Deligne–Lusztig duality on the stack of local systems

Abstract

Motivic decompositions for the Hilbert scheme of points of a K3 surface

Abstract

Extending meromorphic connections to coadmissible ̑𝒟-modules

Abstract

Brauer’s Height Zero Conjecture for principal blocks

Abstract

Four-dimensional complete gradient shrinking Ricci solitons

Abstract

Siegel domains over Finsler symmetric cones

Abstract

Basis divisors and balanced metrics

Abstract

Erratum to The braided Thompson's groups are of type F∞ (J. reine angew. Math. 718 (2016), 59–101)

Erratum to The braided Thompson's groups are of type F_∞ (J. reine angew. Math. 718 (2016), 59–101)