Dmitry Logachev
Simon Bolivar University,Venezuela
Anderson T-motives - a parallel world to abelian varieties.
Abstract: The purpose of the lecture is to give definitions, to describe properties and to state some research problems in the theory of Anderson T-motives (generalizations of Drinfeld modules). They are analogs of abelian varieties over the global functional fields. It turns out that most (probably all) notions of the theory of abelian varieties have their analogs in the theory of Anderson T-motives, although in many cases this analogy is far to be direct and straightforward. For example, attached to an Anderson T-motive M is a lattice in a vector space over the functional field analog of $C$, a Tate module T_l(M) together with the action of a Galois group, etc. For example, we have analogs of Eichler-Shimura congruence relations for reductions of moduli varieties of Drinfeld modules. All definitions will be given from the very beginning, no preliminary knowledge on the arithmetic of global functional fields is required.