Integrating Hasse-Schmidt derivations
The authors study ``integrating (that is, expanding to a Hasse-Schmidt derivation) derivations and more generally truncated Hasse-Schmidt derivations (HS derivations, for short), satisfying iterativity conditions given by formal group laws''. In particular, the authors concentrate their attention on the additive and multiplicative group laws. Such formal group laws give the possibility to reinterpret classical results on derivations in a new way. On the other hand one of the main motivation of the authors ``for considering this topic'' was to study ``other theories of existentially closed fields with HS derivations''. The notion of the Hasse-Schmidt derivation was introduced by \textit{H. Hasse} and \textit{F. K. Schmidt} in 1937 [J. Reine Angew. Math. 177, 215--237 (1937; Zbl 0017.10101; JFM 63.0098.01)], under the name of ``higher derivation'', and the topic was widely studied by Hideyuki Matsumura whose results on this subject have been fundamental for the development of the algebraic theory of derivations. Indeed, the main result in the paper is a generalization of a theorem of Matsumura via group scheme actions.
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