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An analogy between abelian Anderson T-motives of rank r and dimension n , and abelian varieties over C with multiplication by an imaginary quadratic field K, of dimension r and of signature (n, r − n), permits us to get two elementary results in the theory of abelian varieties. Firstly, we can associate to this abelian variety a (roughly speaking) K-vector(More)
We introduce the notion of duality for an abelian Anderson T-motive M. Main results of the paper (all M have N = 0): 1. Algebraic duality implies analytic duality (Theorem 4.4). Explicitly, this means that a Siegel matrix of the dual of a uniformizable M is the minus transposed of a Siegel matrix of M. 2. There is a 1 – 1 correspondence between pure(More)
There exist conjectural formulas on relations between L-functions of submotives of Shimura varieties and automorphic representations of the corresponding reduc-tive groups, due to Langlands — Arthur. In the present paper these formulas are used in order to get explicit relations between eigenvalues of p-Hecke operators (generators of the p-Hecke algebra of(More)
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