2017/09/30 by Eric M. Friedlander, Eric Friedlander, Cris Negron
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic group #Algebraic number #Algebraic structures and combinatorial models #Cohomology #Field (mathematics) #Finitely-generated abelian group #Group (periodic table) #Injective function #Isomorphism (crystallography) #Kernel (algebra) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Variety (cybernetics) #math.QA #math.RT
paper · pdf · doi:10.2140/ant.2018.12.1281
published as Alg. Number Th. 12 (2018) 1281-1309 · 27 pages, minor corrections
arxiv created 2018/05/19 · openalex publication_date 2018/07/31 · arxiv updated 2018/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Consider a field [math] of characteristic [math] , the [math] -th Frobenius kernel [math] of a smooth algebraic group [math] , the Drinfeld double [math] of [math] , and a finite dimensional [math] -module [math] . We prove that the cohomology algebra [math] is finitely generated and that [math] is a finitely generated module over this cohomology algebra. We exhibit a finite map of algebras [math] , which offers an approach to support varieties for [math] -modules. For many examples of interest, [math] is injective and induces an isomorphism of associated reduced schemes. For [math] an irreducible [math] -module, [math] enables us to identify the support variety of [math] in terms of the support variety of [math] viewed as a [math] -module.