Galois actions on the pro-l-unipotent fundamental group

Abstract

This paper establishes restrictions on the possible Galois actions on the pro-l-unipotent fundamental group of a smooth variety X of good reduction over a local field K. In particular, if X is proper and l is not equal to the residue characteristic p of K, then this action is uniquely determined by the action on cohomology. A similar result for l=p is then proved via a comparison theorem between the crystalline and pro-p homotopy types.

26 pages; v2 semi-stable claims withdrawn; v3 references updated; v4 corrected sections 1.4 & 1.5

References in corpus (1)

• The structure of the pro-l-unipotent fundamental group of a smooth variety