Real and p-adic Picard-Vessiot fields

被引：9

作者：

Crespo, Teresa ^{[1
]}

Hajto, Zbigniew ^{[2
]}

van der Put, Marius ^{[3
]}

机构：

[1] Univ Barcelona, Dept Algebra & Geometria, Gran Via Corts Catalanes, E-08007 Barcelona, Spain

[2] Jagiellonian Univ, Fac Math & Comp Sci, Ul Prof S Lojasiewicza 6, PL-30348 Krakow, Poland

[3] Univ Groningen, Dept Math, POB 407, NL-9700 AK Groningen, Netherlands

来源：

MATHEMATISCHE ANNALEN | 2016年 / 365卷 / 1-2期

关键词：

11E10; 11R34; 12D15; 34M50;

D O I：

10.1007/s00208-015-1272-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider differential modules over real and p-adic differential fields K such that its field of constants k is real closed (resp., p-adically closed). Using P. Deligne's work on Tannakian categories and a result of J.-P. Serre on Galois cohomology, a purely algebraic proof of the existence and unicity of real (resp., p-adic) Picard-Vessiot fields is obtained. The inverse problem for real forms of a semi-simple group is treated. Some examples illustrate the relations between differential modules, Picard-Vessiot fields and real forms of a linear algebraic group.

引用

页码：93 / 103

页数：11

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