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Galois representations and Hecke operators associated with the mod $p$ cohomology of $GL(1,\mathbb {Z})$ and $GL(2,\mathbb {Z})$


Author: Avner Ash
Journal: Proc. Amer. Math. Soc. 125 (1997), 3209-3212
MSC (1991): Primary 11F75
DOI: https://doi.org/10.1090/S0002-9939-97-04085-9
MathSciNet review: 1422842
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that any Hecke eigenclass in the mod $p$ cohomology of a congruence subgroup of $GL(1,\mathbb {Z})$ or $GL(2,\mathbb {Z})$ has attached to it a mod $p$ Galois representation such that the characteristic polynomial of a Frobenius element at a prime $l$ equals the Hecke polynomial at $l$.


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  • Avner Ash, Galois representations attached to mod $p$ cohomology of ${\rm GL}(n,{\bf Z})$, Duke Math. J. 65 (1992), no. 2, 235–255. MR 1150586, DOI https://doi.org/10.1215/S0012-7094-92-06510-0
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Additional Information

Avner Ash
Affiliation: The Ohio State University, Department of Mathematics, 231 W. 18th Ave, Columbus, Ohio 43210
MR Author ID: 205374
Email: ash@math.ohio-state.edu

Received by editor(s): June 23, 1996
Additional Notes: Research partially supported by NSA grant MDA-904-94-2030. This manuscript is submitted for publication with the understanding that the United States government is authorized to reproduce and distribute reprints.
Communicated by: William W. Adams
Article copyright: © Copyright 1997 American Mathematical Society