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

James Newton, Jack A. Thorne

Type: Article

Publication Date: 2016-01-01

Citations: 26

DOI: https://doi.org/10.1017/fms.2016.16

Abstract

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.

Locations

Forum of Mathematics Sigma - View - PDF
arXiv (Cornell University) - View - PDF
Research Portal (King's College London) - View - PDF
Apollo (University of Cambridge) - View - PDF
Oxford University Research Archive (ORA) (University of Oxford) - View - PDF

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Works Cited by This (35)

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+	Arithmetical compactification of mixed Shimura varieties	1990	Richard Pink
+	Potential automorphy and the Leopoldt conjecture	2014	Chandrashekhar Khare Jack A. Thorne
+ PDF Chat	Equivariant Sheaves and Functors	1994	Joseph Bernstein Valery A. Lunts
+ PDF Chat	The <i>p</i>-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings	2014	Gaëtan Chenevier
+	Cohomology of Number Fields	2008	Jürgen Neukirch Alexander Schmidt Kay Wingberg
+	Reductive groups over local fields	1979	Jacques Tits
+	Fundamental Algebraic Geometry	2006	Barbara Fantechi Lothar Göttsche Luc Illusie Steven L. Kleiman Nitin Nitsure Angelo Vistoli
+	Representations of Algebraic Groups	2007	Jens Carsten Jantzen
+	Cohomology of sheaves	1984	Birger Iversen
+	Étale Cohomology of Rigid Analytic Varieties and Adic Spaces	1996	Roland Huber