ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 11 Ramachandran, Niranjan, University of Michigan A conjecture of Deligne For any algebraic scheme X of dimension N over a perfect field, we construct one-motives L^{n}(X) for n between 0 and N + 1; these one-motives are well-defined up to isogeny. This purely algebraic construction has two consequences:

1) Over the complex numbers, it almost solves a conjecture of P. Deligne ( Hodge III, 10.4) about the algebraic definition of one-motives that he constructs using the mixed Hodge structure on H^{n}(X; Z(1)).

2) Over finite fields, one obtains independence results for the action of Frobenius on parts of the cohomology of arbitrary varieties.