Xiaotao Sun, Chinese Academy of Sciences, Beijing

Etale fundmental groups and D-modules in characteristic p > 0

Abstract

This is a joint work with H. Esnault. For a smooth projective variety over an algebraically closed field of characteristic p > 0, we proved: (1) All the irreducible D-modules have rank 1 if and only if the commutator of the etale fundamental group is a pro-p-group. (2) Every D-module is a direct sum of rank 1 D-modules if and only if the etale fundamental group is abelian with no non-trivial p-power quotient. The above theorem with a result of Esnault-Mehta (Invent. math. 181 (2010), 449-465) together proves completely a conjecture of D. Gieseker (D. Gieseker: Ann. Sc. Norm. Super. Pisa, 4 (1975), 1-31).