Weights of simple Lie algebras in the cohomology of algebraic varieties

This article studies representations of semisimple Lie algebras arising naturally in the $l$-adic cohomology of algebraic varieties defined over global fields. A conjecture is formulated about the restrictions the index of the cohomology space and the Hodge numbers of a variety impose on the weights of a represention. The conjecture is proved for ordinary varieties over function fields. An analog of the conjecture is valid for the rational cohomology of varieties defined over the field of complex numbers.
Bibliography: 41 titles.