$p$-adic formulas and unit root $F$-subcrystals of the hypergeometric system
| dc.creator | Baldassarri, Francesco | |
| dc.creator | Cailotto, Maurizio | |
| dc.date | 2004-09-13 | |
| dc.date.accessioned | 2026-07-07T05:12:04Z | |
| dc.date.available | 2026-07-07T05:12:04Z | |
| dc.description | 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 $F(a,b,c;1)$. | |
| dc.description | 20 pages, Plain TeX | |
| dc.identifier | https://arxiv.org/abs/math/0409207 | |
| dc.identifier | http://arxiv.org/abs/math/0409207 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72455 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11T23;11S31;12H25;14F30 | |
| dc.title | $p$-adic formulas and unit root $F$-subcrystals of the hypergeometric system | |
| dc.type | text |