Tannakian properties of unit Frobenius-modules

Abstract

We show that unit ${\mathcal{O}}_{F,X}^{\Lambda }$-modules of Emerton and Kisin provide an analogue of locally constant sheaves in the context of Böckle-Pink $\Lambda$-crystals. For example they form a tannakian category if the coefficient algebra $\Lambda$ is a field. Our results hold for a big class of coefficien algebras which includes Drinfeld rings, and for arbitary locally noetherian base schemes.

arXiv comment10 pages; lemma 2.3 replaced with a reference to Bourbaki; some misprints corrected