Lie Algebras of Pro-Affine Algebraic Groups

Abstract

Abstract. We extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed field K of characteristic 0. However, some modifications are needed in some extensions. So we introduce the pro-discrete topology on the Lie algebra L(G) of the pro-affine algebraic group G over K, which is discrete in the finite-dimensional case and linearly compact in general. As an example, if L is any sub Lie algebra of L(G), we show that the closure of

Connections on trivial vector bundles over projective schemes

“…All that follows in this section is, in essence, due to Hochschild [12]; since he expressed himself without using group schemes and his ideas are spread out in several papers, we shall briefly condense his theory in what follows. The reader should also consult [22], where some results reviewed here also appear.…”

Connections on trivial vector bundles over projective schemes

“…All that follows in this section is, in essence, due to Hochschild [Ho59]; since he expressed himself without using group schemes and his ideas are spread out in several papers, we shall briefly condense his theory in what follows. The reader should also consult [Na02], where some results reviewed here also appear.…”