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 formulae 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.
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