2004/09/13 by Francesco Baldassarri, Baldassarri, Francesco, Maurizio Cailotto +1
Mathematics · #11S31 #11T23 #12H25 #14F30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.AG #math.NT #msc:11S31 #msc:11T23 #msc:12H25 #msc:14F30
paper · pdf · doi:10.48550/arxiv.math/0409207
20 pages, Plain TeX
arxiv created 2004/09/13 · openalex publication_date 2004/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the notion of \it Dwork family of logarithmic F-crystals, a typical example of which is the family of Gauss hypergeometricdifferential systems, viewed as parametrized by their exponents of algebraic monodromy. The p-adic analytic dependence of the Frobenius operation upon those exponents, is Dwork's "Boyarsky Principle". We discuss, in favorable cases, the p-adic analytic continuation of the unit root F-subcrystal in the open tube of a singularity, uniformly w.r.t. the exponents. We obtain a conceptual proof of the Koblitz-Diamond formula p-adically analog to Gauss' evaluation of F(a,b,c;1).