2016/05/31 by Masha Vlasenko
Mathematics · #math.AG #math.NT
paper · pdf · doi:10.1016/j.indag.2018.07.004
This paper is an extension of my earlier preprint 'Explicit p-adic unit-root formulas for hypersurfaces' (arXiv:1501.04280 [math.NT] )
arxiv created 2018/04/17 · arxiv updated 2018/07/24
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.)