Cohomology with twisted one-dimensional coefficients for congruence subgroups of SL4 (Z) and Galois representations

JOURNAL OF ALGEBRA

卷:553

Article

Ash, Avner¹  Gunnells, Paul E.²  McConnell, Mark³ 

[1] Boston Coll, Chestnut Hill, MA 02445 USA

[2] Univ Massachusetts, Amherst, MA 01003 USA

[3] Princeton Univ, Princeton, NJ 08540 USA

关键词: Cohomology of arithmetic groups;    Galois representations;    Voronoi complex;    Steinberg module;    Modular symbols;   

DOI  :  10.1016/j.jalgebra.2020.01.024

来源: Elsevier

【 摘 要 】

We extend the computations in [2-4] to find the cohomology in degree five of a congruence subgroup of SL4 (Z) with coefficients in a field twisted by a nebentype character, along with the action of the Hecke algebra on the cohomology. This is the top cuspidal degree. For each Hecke eigenclass we find, we produce the unique Galois representation that appears to be attached to it. The computations require serious modifications to our previous algorithms. Nontrivial coefficients add a layer of complication to our data structures. New possibilities must be taken into account in the Galois Finder, the code that finds the Galois representations. We have improved the Galois Finder to report when the attached Galois representation is uniquely determined by our data. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free