A-hypergeometric series and a p-adic refinement of the Hasse-Witt matrix

2020/01/20 by Alan Adolphson, Steven Sperber, Adolphson, Alan +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2001.07280

28 pages

arxiv created 2020/01/20 · arxiv updated 2020/01/22

Abstract

We identify the p-adic unit roots of the zeta function of a projective hypersurface over a finite field of characteristic p as the eigenvalues of a product of special values of a certain matrix of p-adic series. That matrix is a product F(Λ^p)^-1F(Λ), where the entries in the matrix F(Λ) are A-hypergeometric series with integral coefficients and F(Λ) is independent of p.

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