The V-filtration for tame unit $F$-crystals
Algebraic Geometry
2011-10-25 v2 Number Theory
Abstract
Let X be a smooth variety over an algebraically closed field of characteristic p > 0, Z a smooth divisor, and j : U = X\Z --> X the natural inclusion. An axiomatizing of the properties of a V -filtration on a unit F-crystal is proposed and is proven to determine a unique filtration. It is shown that if M is a tame unit F-crystal on U then such a V -filtration along Z exists on j_*M. The degree zero component of the associated graded module is proven to be the (unipotent) nearby cycles functor of Grothendieck and Deligne under the Emerton-Kisin Riemann-Hilbert correspondence. A few applications to A^1 and gluing are then discussed.
Keywords
Cite
@article{arxiv.1110.3269,
title = {The V-filtration for tame unit $F$-crystals},
author = {Theodore J. Stadnik},
journal= {arXiv preprint arXiv:1110.3269},
year = {2011}
}
Comments
Comments welcome; v2 fixes minor typesetting errors