On the geometric theory of \(G\)-functions. The Chudnovsky theorem in several variables (Q5927637)

The author gives an introduction to the theory of several-variable \(G\)-functions, continuing fundamental works of André, Baldassarri and Dwork. The approach is geometric, based on the notions of differential modules and connections. The main result is an elegant generalization of the theorem of \textit{D. V. Chudnovsky} and \textit{G. V. Chudnovsky} [in: Number theory, Semin. New York 1983--84, Lect. Notes Math. 1135, 52-100 (1985; Zbl 0565.14010)] that the minimal differential operator annihilating a given \(G\)-function has only regular singularities and all corresponding exponents are rational. The paper is very well written and contains interesting suggestions for further applications in the theory of arithmetic operators.