April 5
Speaker: Andrew Lamoureux (Binghamton)
Title: Arithmetic Differential Operators over Compact DVRs, part 2
Abstract: This is the continuation of the March 22 talk. In 2011, Alexandru Buium, Claire C. Ralph, and Santiago Simanca proved that a map f: Z_p → Z_p is an 'arithmetic differential operator or order m' if and only if it is 'analytic of level m'. Both notions can be generalized first to maps f: R^d → R, where R is a compact DVR, and then to maps f: X(R) → Y(R), where X and Y are two smooth affine schemes of finite type over R. In this talk, we will see that these notions are still equivalent in this more general context and that every analytic map of manifolds f:X(R) → Y(R) is analytic of level m for some m.