Hecke correspondences and Betti cohomology groups for smooth compactifications of Hilbert modular varieties of dimension <=3

被引：0

作者：

Hatada, K ^{[1
]}

机构：

[1] GIFU UNIV, FAC EDUC, DEPT MATH, GIFU 50111, JAPAN

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 1996年 / 72卷 / 08期

关键词：

D O I：

10.3792/pjaa.72.189

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider Betti cohomology groups of smooth toroidal compactifications of Hilbert modular varieties and representations of Hecke correspondences on them. We study absolute values and zeta functions of eigenvalues of those operators for varieties of dimension less than or equal to 3. Our main results are Theorems 1 similar to 6 below.

引用

页码：189 / 193

页数：5

共 20 条

[1] CORRESPONDENCES FOR HECKE RINGS AND L-ADIC COHOMOLOGY GROUPS ON SMOOTH COMPACTIFICATIONS OF SIEGEL MODULAR VARIETIES
HATADA, K
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1989, 65 (02) : 62 - 65
[2] Extensions in the cohomology of Hilbert modular varieties
Davidescu, Cosmin
Scholl, Anthony J.
[J]. MUENSTER JOURNAL OF MATHEMATICS, 2020, 13 (02): : 509 - 518
[3] Equidistribution of Hecke eigenforms on the Hilbert modular varieties
Liu, Sheng-Chi
[J]. JOURNAL OF NUMBER THEORY, 2007, 127 (01) : 1 - 9
[4] Compactifications of Iwahori-level Hilbert modular varieties
Diamond, Fred
[J]. JOURNAL OF NUMBER THEORY, 2024, 263 : 255 - 296
[5] Intersection numbers of Hecke cycles on Hilbert modular varieties
Getz, Jayce
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2007, 129 (06) : 1623 - 1658
[6] EIGENVALUES OF HECKE OPERATORS ON HILBERT MODULAR GROUPS
Bruggeman, Roelof W.
Miatello, Roberto J.
[J]. ASIAN JOURNAL OF MATHEMATICS, 2013, 17 (04) : 729 - 757
[7] ON THE COHOMOLOGY GROUPS OF LOCAL SYSTEMS OVER HILBERT MODULAR VARIETIES VIA HIGGS BUNDLES
Mueller-Stach, Stefan
Sheng, Mao
Ye, Xuanming
Zuo, Kang
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2015, 137 (01) : 1 - 35
[8] Motivic Action on Coherent Cohomology of Hilbert Modular Varieties
Horawa, Aleksander
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (12) : 10439 - 10531
[9] On the étale cohomology of Hilbert modular varieties with torsion coefficients
Caraiani, Ana
Tamiozzo, Matteo
[J]. COMPOSITIO MATHEMATICA, 2023, 159 (11) : 2279 - 2325
[10] Galois representations modulo p and cohomology of Hilbert modular varieties
Dimitrov, M
[J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2005, 38 (04): : 505 - 551

← 1 2 →