Zeta functions over finite fields- An exposition of Dwork's methods

2020/12/03 by Martin Ortiz Ramirez, Ramirez, Martin Ortiz
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2012.01809

openalex publication_date 2020/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper reviews Dwork's p-adic analytic methods used in the Weil Conjectures. The first two chapters review a version of his proof of the rationality conjecture. The rest of the paper is devoted to Dwork's original cohomological methods, along with some p-adic functional analysis. The last chapter applies what is developed to an example of Dwork's family of hypersurfaces.

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