Relative cohomology of cuspidal forms on PEL-type Shimura varieties

被引：7

作者：

Lan, Kai-Wen ^{[1
]}

Stroh, Benoit ^{[2
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Paris 13, CNRS, LAGA, F-93430 Villetaneuse, France

来源：

ALGEBRA & NUMBER THEORY | 2014年 / 8卷 / 08期

基金：

美国国家科学基金会;

关键词：

Shimura varieties; vanishing theorem; toroidal compactification; minimal compactification; cuspidal forms; TORSION AUTOMORPHIC SHEAVES; VANISHING THEOREMS;

D O I：

10.2140/ant.2014.8.1787

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a short proof that, for PEL-type Shimura varieties, subcanonical extensions of automorphic bundles, whose global sections over toroidal compactifications of Shimura varieties are represented by cuspidal automorphic forms, have no higher direct images under the canonical morphism to the minimal compactification, in characteristic zero or in positive characteristics greater than an explicitly computable bound.

引用

收藏

页码：1787 / 1799

页数：13

相关论文

共 26 条

[11] On the generic part of the cohomology of non-compact unitary Shimura varieties [J].

Caraiani, Ana ;

Scholze, Peter .

ANNALS OF MATHEMATICS, 2024, 199 (02) :483-590

[12] WEIGHT ZERO EISENSTEIN COHOMOLOGY OF SHIMURA VARIETIES VIA BERKOVICH SPACES [J].

Harris, Michael .

PACIFIC JOURNAL OF MATHEMATICS, 2014, 268 (02) :275-281

[13] Integral models in unramified mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part II [J].

Vasiu, Adrian .

MATHEMATISCHE NACHRICHTEN, 2014, 287 (14-15) :1756-1773

[14] Supercuspidal part of the mod l cohomology of GU(1, n-1)-Shimura varieties [J].

Shin, Sug Woo .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2015, 705 :1-21

[15] On the superspecial loci of orthogonal type Shimura varieties [J].

Wang, Haining .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2023, 19 (08) :1801-1831

[16] ON THE l-ADIC COHOMOLOGY OF SOME p-ADICALLY UNIFORMIZED SHIMURA VARIETIES [J].

Shen, Xu .

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2018, 17 (05) :1197-1226

[17] MOD p POINTS ON SHIMURA VARIETIES OF ABELIAN TYPE [J].

Kisin, Mark .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 30 (03) :819-914

[18] p-adic Hodge-theoretic properties of etale cohomology with mod p coefficients, and the cohomology of Shimura varieties [J].

Emerton, Matthew ;

Gee, Toby .

ALGEBRA & NUMBER THEORY, 2015, 9 (05) :1035-1088

[19] STRATIFICATIONS IN GOOD REDUCTIONS OF SHIMURA VARIETIES OF ABELIAN TYPE [J].

Shen, Xu ;

Zhang, Chao .

ASIAN JOURNAL OF MATHEMATICS, 2022, 26 (02) :167-226

[20] Nonemptiness of Newton strata of Shimura varieties of Hodge type [J].

Lee, Dong Uk .

ALGEBRA & NUMBER THEORY, 2018, 12 (02) :259-283