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Affine ind-varieties are infinite dimensional generalizations of algebraicvarieties which appear naturally in many different contexts, in particular inthe study of automorphism groups of affine spaces. In this article we introduceand develop the basic algebraic theory of topologically integrable derivationsof complete topological rings. We establish a bijective algebro-geometriccorrespondence between additive group actions on affine ind-varieties andtopologically integrable derivations of their coordinate pro-rings whichextends the classical fruitful correspondence between additive group actions onaffine varieties and locally nilpotent derivations of their coordinate rings.

Topologically integrable derivations and additive group actions on affine ind-schemes