TORSION GALOIS REPRESENTATIONS OVER CM FIELDS AND HECKE ALGEBRAS IN THE DERIVED CATEGORY. (21st July 2016) - NEWTON, JAMES; THORNE, JACK A.
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.