SPEAKER:     Arvind Nair, Tata Institute

TITLE:    On the motive of a Shimura variety

ABSTRACT:
Shimura varieties are higher-dimensional generalizations of modular curves and their cohomology groups are a source of interesting Galois representations which can be related to modular forms. (In the modular curve case this is the relation between H^1 of the curve and weight 2 modular forms due to Eichler and Shimura.) In this situation, one wants something more than a Galois representation, namely a motive. (In the modular curve case this is roughly speaking the Jacobian of the curve rather than simply its H^1.) I will explain what this means and how to do this when the Shimura variety is noncompact (as the most natural examples are), at least for the most interesting part (i.e. the tempered part) of the cohomology.