Higher Hasse--Witt matrices
Number Theory
2018-07-24 v3 Algebraic Geometry
Abstract
We prove a number of p-adic congruences for the coefficients of powers of a multivariate polynomial f(x) with coefficients in a ring R of characteristic zero. If the Hasse--Witt operation is invertible, our congruences yield p-adic limit formulas which conjecturally describe the Gauss--Manin connection and the Frobenius operator on the unit-root crystal attached to f(x). As a second application, we associate with f(x) formal group laws over R. Under certain assumptions these formal group laws are coordinalizations of the Artin--Mazur functors. (This is a final version which we send for a publication.)
Cite
@article{arxiv.1605.06440,
title = {Higher Hasse--Witt matrices},
author = {Masha Vlasenko},
journal= {arXiv preprint arXiv:1605.06440},
year = {2018}
}
Comments
This paper is an extension of my earlier preprint 'Explicit p-adic unit-root formulas for hypersurfaces' (arXiv:1501.04280 [math.NT] )