On the zeta function of a projective complete intersection

2006/10/06 by Alan Adolphson, Steven Sperber, Adolphson, Alan +1
Mathematics · #11M38 #14F30 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11M38 #msc:14F30

paper · pdf · doi:10.48550/arxiv.math/0610230

24 pages, no figures

arxiv created 2006/10/06 · openalex publication_date 2006/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute a basis for the p-adic Dwork cohomology of a smooth complete intersection in projective space over a finite field and use it to give p-adic estimates for the action of Frobenius on this cohomology. In particular, we prove that the Newton polygon of the characteristic polynomial of Frobenius lies on or above the associated Hodge polygon. This result was first proved by B. Mazur using crystalline cohomology.

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