Documenta Mathematica最新文献_第4页

Equivariant Chow–Witt groups and moduli stacks of elliptic curves 椭圆曲线的等变Chow-Witt群和模堆

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2023-08-16 DOI: 10.4171/dm/911

Andrea Di Lorenzo, L. Mantovani

引用次数: 0

Erratum to “The line bundles on moduli stacks of principal bundles on a curve” “曲线上主束的模堆上的线束”的勘误

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2023-08-16 DOI: 10.4171/dm/921

I. Biswas, N. Hoffmann

引用次数: 0

On the minus component of the equivariant Tamagawa number conjecture for $mathbb{G}_m$ $mathbb{G}_m$的等变Tamagawa数猜想的负分量

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2023-08-16 DOI: 10.4171/dm/914

Mahiro Atsuta, T. Kataoka

引用次数: 0

Slopes of $F$-isocrystals over abelian varieties $F$-同晶在阿贝尔变种上的斜率

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2023-08-07 DOI: 10.4171/dm/910

Marco d’Addezio

引用次数: 0

Derivatives of Beilinson–Flach classes, Gross–Stark formulas and a $p$-adic Harris–Venkatesh conjecture Beilinson-Flach类的导数，Gross-Stark公式和$p$-adic Harris-Venkatesh猜想

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2023-08-07 DOI: 10.4171/dm/905

Óscar Rivero

引用次数: 0

Tori over number fields and special values at $s=1$ 在$s=1$处，Tori over number字段和特殊值

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2022-10-17 DOI: 10.4171/dm/906

Adrien Morin

{"title":"Tori over number fields and special values at $s=1$","authors":"Adrien Morin","doi":"10.4171/dm/906","DOIUrl":"https://doi.org/10.4171/dm/906","url":null,"abstract":"We define a Weil-'etale complex with compact support for duals (in the sense of the Bloch dualizing cycles complex $mathbb{Z}^c$) of a large class of $mathbb{Z}$-constructible sheaves on an integral $1$-dimensional proper arithmetic scheme flat over $mathrm{Spec}(mathbb{Z})$. This complex can be thought of as computing Weil-'etale homology. For those $mathbb{Z}$-constructible sheaves that are moreover tamely ramified, we define an\"additive\"complex which we think of as the Lie algebra of the dual of the $mathbb{Z}$-constructible sheaf. The product of the determinants of the additive and Weil-'etale complex is called the fundamental line. We prove a duality theorem which implies that the fundamental line has a natural trivialization, giving a multiplicative Euler characteristic. We attach a natural $L$-function to the dual of a $mathbb{Z}$-constructible sheaf; up to a finite number of factors, this $L$-function is an Artin $L$-function at $s+1$. Our main theorem contains a vanishing order formula at $s=0$ for the $L$-function and states that, in the tamely ramified case, the special value at $s=0$ is given up to sign by the Euler characteristic. This generalizes the analytic class number formula for the special value at $s=1$ of the Dedekind zeta function. In the function field case, this a theorem of arXiv:2009.14504.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79766134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reduction of structure to parabolic subgroups 抛物子群结构的约化

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2022-03-08 DOI: 10.4171/dm/901

Danny Ofek

引用次数: 0

The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines 与一组中央直线相切的微分算子代数的Hochschild上同调

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2022-01-01 DOI: 10.4171/dm/887

F. Kordon, M. Suárez-Álvarez

引用次数: 1

On class number relations and intersections over function fields