Support varieties for infinitesimal group schemes
نویسندگان
چکیده
منابع مشابه
Geometry of Infinitesimal Group Schemes
We consider aane group schemes G over a eld k of characteristic p > 0. Equivalently , we consider nitely generated commutative k-algebras kG] (the coordinate algebra of G) endowed with the structure of a Hopf algebra. The group scheme G is said to be nite if kG] is nite dimensional (over k) and a nite group scheme is said to be innnitesimal if the ((nite dimensional) algebra kG] is local. A rat...
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Consider a field k of characteristic p > 0, G(r) the r-th Frobenius kernel of a smooth algebraic group G, DG(r) the Drinfeld double of G(r), and M a finite dimensional DG(r)-module. We prove that the cohomology algebra H(DG(r), k) is finitely generated and that H(DG(r),M) is a finitely generated module over this cohomology algebra. We exhibit a finite map of algebras θr : H(G(r), k) ⊗ S(g) → H(...
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This article is concerned with Galois theory for iterative differential fields (ID-fields) in positive characteristic. More precisely, we consider purely inseparable Picard-Vessiot extensions, because these are the ones having an infinitesimal group scheme as iterative differential Galois group. In this article we prove a necessary and sufficient condition to decide whether an infinitesimal gro...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1997
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-97-00239-7