Abstract
We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group
$\unicode[STIX]{x1D6E4}$
. Under favorable conditions, the cohomology is freely generated in a single degree over this graded Hecke algebra.
From this construction we extract an action of certain
$p$
-adic Galois cohomology groups on
$H^{\ast }(\unicode[STIX]{x1D6E4},\mathbf{Q}_{p})$
, and formulate the central conjecture: the motivic
$\mathbf{Q}$
-lattice inside these Galois cohomology groups preserves
$H^{\ast }(\unicode[STIX]{x1D6E4},\mathbf{Q})$
.
Publisher
Cambridge University Press (CUP)
Subject
Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Analysis
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