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TORSION GALOIS REPRESENTATIONS OVER CM FIELDS AND HECKE ALGEBRAS IN THE DERIVED CATEGORY

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  21 July 2016

JAMES NEWTON  and
JACK A. THORNE
JAMES NEWTON
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK; j.newton@imperial.ac.uk
JACK A. THORNE
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, UK; thorne@dpmms.cam.ac.uk

Abstract

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We construct algebras of endomorphisms in the derived category of the cohomology of arithmetic manifolds, which are generated by Hecke operators. We construct Galois representations with coefficients in these Hecke algebras and apply this technique to sharpen recent results of P. Scholze.

MSC classification

Primary: 11F75: Cohomology of arithmetic groups 11F80: Galois representations
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 4 , 2016 , e21
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2016

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