Commutative algebraic groups up to isogeny. II

Michel Brion (1)

1 IF - Institut Fourier

This paper develops a representation-theoretic approach to theisogeny categoryCof commutative group schemes of finite type over a fieldk,studied in our earlier work. We construct a ringRsuch thatCis equivalent tothe categoryR-mod of all leftR-modules of finite length. We also constructan abelian category ofR-modules,R- ̃mod, which is hereditary, has enoughprojectives, and containsR-mod as a Serre subcategory; this yields a moreconceptual proof of the main result of our earlier work, asserting thatCishereditary. We show thatR- ̃mod is equivalent to the isogeny category ofcommutative quasi-compactk-group schemes.

Domaines: Mathématiques [math]

Michel Brion. Commutative algebraic groups up to isogeny. II. Representations of Algebras, 705, 2018, Contemporary Mathematics, 978-1-4704-3576-9. ⟨hal-02020768⟩