FRANCESCO BALDASSARRI and MAURIZIO CAILOTTO

p-adic formulas and unit root F-subcrystals of the hypergeometric system

Pages: 33-65
Received: 7 September 2004   
Mathematics Subject Classification (2000): 11T23 - 11S31 - 12H25 - 14F30

Abstract: In this paper, we define the notion of it Dwork family of logarithmic F-crystals, a typical example of which is the family of Gauss hypergeometric differential 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.Using these ideas, we obtain a conceptual proof of the Koblitz-Diamond formula p-adically analog to Gauss' evaluation of F(a,b,c;1). p>