2016/12/12 by Michel Brion, Brion, Michel
Mathematics · #14K02 #14L15 #18E35 #20G07 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.AG #math.RT #msc:14K02 #msc:14L15 #msc:18E35 #msc:20G07
paper · pdf · doi:10.48550/arxiv.1612.03634
35 pages. Minor changes, to appear at the proceedings of the 2016 International Conference on Representations of Algebras
openalex publication_date 2016/12/12 · arxiv created 2017/04/11 · arxiv updated 2017/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper develops a representation-theoretic approach to the isogeny category \underlineC of commutative group schemes of finite type over a field k, studied in arXiv:1602:00222. We construct a ring R such that \underlineC is equivalent to the category R-mod of all left R-modules of finite length. We also construct an abelian category of R-modules, R-\widetilde\rm mod, which is hereditary, has enough projectives, and contains R-mod as a Serre subcategory; this yields a more conceptual proof of the main result of [loc. cit.], asserting that \underlineC is hereditary. We show that R-\widetilde\rm mod is equivalent to the isogeny category of commutative quasi-compact k-group schemes.