On the Cohomology of GL2 and SL2 over Imaginary Quadratic Fields

被引：0

作者：

Gangl, Herbert ^{[1
]}

Gunnells, Paul E. ^{[2
]}

Hanke, Jonathan ^{[3
]}

Yasaki, Dan ^{[3
]}

机构：

[1] Dept Math Sci, Durham, England

[2] Univ Massachusetts, Dept Math & Stat, LGRT 1115L, Amherst, MA USA

[3] Univ North Carolina Greensboro, Dept Math & Stat, Greensboro, NC USA

来源：

EXPERIMENTAL MATHEMATICS | 2024年

关键词：

cohomology of arithmetic groups; Voronoi reduction theory; linear groups over imaginary quadratic fields; HOMOLOGICAL TORSION; BIANCHI; GROWTH; PSL2;

D O I：

10.1080/10586458.2024.2379797

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We report on computations of the cohomology of GL(2)(O-D) and SL2(O-D) , where D < 0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We use the technique of homology of Voronoi complexes, and our computations recover the integral cohomology away from the primes 2, 3. We observed exponential growth in the torsion subgroup of H (2) as |D| increases, and compared our data to bounds of Rohlfs.

引用

页数：18

共 11 条

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