2010 Fiscal Year Final Research Report

Application of p-adic differential equations to number theory

Research Project

Project/Area Number	19540010
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Chiba University
Principal Investigator	MATSUDA Shigeki Chiba University, 大学院・理学研究科, 准教授 (90272301)
Project Period (FY)	2007 – 2010
Keywords	数論
Research Abstract	Let k be a filed of Laurent series with several variables over an algebraically closed field of positive characteristic and let E be a complete discrete valuation ring of equal characteristic with residue field k. We defined a filtration for a differential module over the Robba ring with residue filed E with respect to the irregularity, which generalized classical filtration defined by Christol and Mebkhout. Then we showed that the filtration coincides with the filtration that comes from the Abbes-Saito filtration on the solution space regarded as Galois module when the differential module can be trivialized by the finite separable extension of the residue field E.

(2 results)