A Splitting of the Frobenius Morphism on the Whole Algebra of Distributions of SL(2)

Michel Gros (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We define, over k = F(p), a splitting of the Frobenius morphism Fr : Dist (G) -> Dist (G) on the whole Dist (G), the algebra of distributions of the k-algebraic group G := SL(2). This splitting is compatible (and lifts) the theory of Frobenius descent for arithmetic D- modules over X := P(k)(1).

Mots clés: Frobenius splitting; Algebra of distributions

Domaines: Géométrie algébrique [math.AG]

Michel Gros. A Splitting of the Frobenius Morphism on the Whole Algebra of Distributions of SL(2). Algebras and Representation Theory, 2012, 15 (1), pp.109-118. ⟨10.1007/s10468-010-9234-6⟩. ⟨hal-00671122⟩