journal: Journal für die reine und angewandte Mathematik

Impact Factor: 1.809

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

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 2023 Issue 796

March 2023

Publicly Available March 1, 2023

Frontmatter

Page range: i-iv

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Open Access February 23, 2023

The Kottwitz conjecture for unitary PEL-type Rapoport–Zink spaces

Alexander Bertoloni Meli, Kieu Hieu Nguyen

Page range: 1-68

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Abstract

In this paper we study the cohomology of PEL-type Rapoport–Zink spaces associated to unramified unitary similitude groups over ℚ p {\operatorname{\mathbb{Q}}_{p}} in an odd number of variables. We extend the results of Kaletha–Minguez–Shin–White and Mok to construct a local Langlands correspondence for these groups and prove an averaging formula relating the cohomology of Rapoport–Zink spaces to this correspondence. We use this formula to prove the Kottwitz conjecture for the groups we consider.

December 9, 2022

Milnor K-theory of p-adic rings

Morten Lüders, Matthew Morrow

Page range: 69-116

Abstract

We study the mod p r {p^{r}} Milnor K -groups of p -adically complete and p -henselian rings, establishing in particular a Nesterenko–Suslin-style description in terms of the Milnor range of syntomic cohomology. In the case of smooth schemes over complete discrete valuation rings we prove the mod p r {p^{r}} Gersten conjecture for Milnor K -theory locally in the Nisnevich topology. In characteristic p we show that the Bloch–Kato–Gabber theorem remains true for valuation rings, and for regular formal schemes in a pro sense.

February 28, 2023

Scrollar invariants, syzygies and representations of the symmetric group

Wouter Castryck, Floris Vermeulen, Yongqiang Zhao

Page range: 117-159

Abstract

We give an explicit minimal graded free resolution, in terms of representations of the symmetric group S d {S_{d}} , of a Galois-theoretic configuration of d points in 𝐏 d - 2 {\mathbf{P}^{d-2}} that was studied by Bhargava in the context of ring parametrizations. When applied to the geometric generic fiber of a simply branched degree d cover of 𝐏 1 {\mathbf{P}^{1}} by a relatively canonically embedded curve C , our construction gives a new interpretation for the splitting types of the syzygy bundles appearing in its relative minimal resolution. Concretely, our work implies that all these splitting types consist of scrollar invariants of resolvent covers. This vastly generalizes a prior observation due to Casnati, namely that the first syzygy bundle of a degree 4 cover splits according to the scrollar invariants of its cubic resolvent. Our work also shows that the splitting types of the syzygy bundles, together with the multi-set of scrollar invariants, belong to a much larger class of multi-sets of invariants that can be attached to C → 𝐏 1 {C\to\mathbf{P}^{1}} : one for each irreducible representation of S d {S_{d}} , i.e., one for each partition of d .

Open Access January 27, 2023

Residual categories of quadric surface bundles

Fei Xie

Page range: 161-199

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Abstract

We show that the residual categories of quadric surface bundles are equivalent to the (twisted) derived categories of some scheme under the following hypotheses. • Case 1: The quadric surface bundle has a smooth section. • Case 2: The total space of the quadric surface bundle is smooth and the base is a smooth surface. We provide two proofs in Case 1 describing the scheme as the hyperbolic reduction and as a subscheme of the relative Hilbert scheme of lines, respectively. In Case 2, the twisted scheme is obtained by performing birational transformations to the relative Hilbert scheme of lines. Finally, we apply the results to certain complete intersections of quadrics.

January 27, 2023

Uniqueness of entire graphs evolving by mean curvature flow

Panagiota Daskalopoulos, Mariel Saez

Page range: 201-227

Abstract

In this paper we study the uniqueness of graphical mean curvature flow with locally Lipschitz initial data. We first prove that rotationally symmetric entire graphs are unique, without any further assumptions. Our methods also give an alternative simple proof of uniqueness in the one-dimensional case. In the general case, we establish the uniqueness of entire proper graphs that satisfy a uniform lower bound on the second fundamental form. The latter result extends to initial conditions that are proper graphs over subdomains of ℝ n {\mathbb{R}^{n}} . A consequence of our result is the uniqueness of convex entire graphs, which allow us to prove that Hamilton’s Harnack estimate holds for mean curvature flow solutions that are convex entire graphs.

February 23, 2023

Moduli spaces of complex affine and dilation surfaces

Paul Apisa, Matt Bainbridge, Jane Wang

Page range: 229-243

Abstract

We construct moduli spaces of complex affine and dilation surfaces. Using ideas of Veech [W. A. Veech, Flat surfaces, Amer. J. Math. 115 1993, 3, 589–689], we show that the moduli space 𝒜 g , n ⁢ ( 𝒎 ) {{\mathcal{A}}_{g,n}(\boldsymbol{m})} of genus g affine surfaces with cone points of complex order 𝒎 = ( m 1 ⁢ … , m n ) {\boldsymbol{m}=(m_{1}\ldots,m_{n})} is a holomorphic affine bundle over ℳ g , n {\mathcal{M}_{g,n}} , and the moduli space 𝒟 g , n ⁢ ( 𝒎 ) {{\mathcal{D}}_{g,n}(\boldsymbol{m})} of dilation surfaces is a covering space of ℳ g , n {\mathcal{M}_{g,n}} . We then classify the connected components of 𝒟 g , n ⁢ ( 𝒎 ) {{\mathcal{D}}_{g,n}(\boldsymbol{m})} and show that it is an orbifold- K ⁢ ( G , 1 ) {K(G,1)} , where G is the framed mapping class group of [A. Calderon and N. Salter, Framed mapping class groups and the monodromy of strata of Abelian differentials, preprint 2020].

February 23, 2023

Strominger connection and pluriclosed metrics

Quanting Zhao, Fangyang Zheng

Page range: 245-267

Abstract

In this paper, we prove a conjecture raised by Angella, Otal, Ugarte and Villacampa recently, which states that if the Strominger connection (also known as Bismut connection) of a compact Hermitian manifold is Kähler-like, in the sense that its curvature tensor obeys all the symmetries of the curvature of a Kähler manifold, then the metric must be pluriclosed. What we actually showed is a bit more: for any given Hermitian manifold, the Strominger Kähler-like condition is equivalent to the pluriclosedness of the metric plus the parallelness of the torsion.

February 23, 2023

Lattice cohomology and q-series invariants of 3-manifolds

Rostislav Akhmechet, Peter K. Johnson, Vyacheslav Krushkal

Page range: 269-299

Abstract

In this paper, an invariant is introduced for negative definite plumbed 3-manifolds equipped with a spin c {{}^{c}} -structure. It unifies and extends two theories with rather different origins and structures. One theory is lattice cohomology, motivated by the study of normal surface singularities, known to be isomorphic to the Heegaard Floer homology for certain classes of plumbed 3-manifolds. Another specialization gives BPS q -series which satisfy some remarkable modularity properties and recover SU ⁢ ( 2 ) {{\rm SU}(2)} quantum invariants of 3-manifolds at roots of unity. In particular, our work gives rise to a 2-variable refinement of the Z ^ {\widehat{Z}} -invariant.

Ahead of Print / Just Accepted

Ahead of Print / Just Accepted

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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

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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.

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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
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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.
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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