Exposé de Matthieu Romagny: Smooth affine group schemes over the dual numbers

jeudi 18 mars 2021, 14:00 → 15:00 Europe/Paris

en ligne (https://webconf.lal.cloud.math.cnrs.fr/b/flo-k3r-y9a)

We provide a geometric construction for the equivalence between the category of smooth affine group schemes over the ring of dual numbers k[ε] and the category of
extensions 1 → Lie(G) → E → G → 1 where G is a smooth affine group scheme over k. The equivalence is given by Weil restriction, and we provide a quasi-inverse which we call Weil
extension. As an application, we establish a Dieudonné classification for smooth, commutative, unipotent group schemes over k[ε] when k is a perfect field.