Ober­sem­in­ar "Num­ber The­ory and Arith­met­ic­al Stat­ist­ics": Béranger Seguin (UPB), Al­geb­ra­ic Patch­ing for Be­gin­ners

Location: A3.339
Organizer: Prof. Dr. Jürgen Klüners

Title: Algebraic Patching for Beginners

Abstract: Using the language and the tools of rigid analytic geometry, Harbater (1987) has defined a "patching operation" which can be used to solve the inverse Galois problem over fields like Qₚ(T) or Fₚ((X))(T). Later, Haran and Völklein (1996) rephrased this construction in a purely algebraic language, replacing all geometric arguments with (almost entirely) explicit constructions. Our goal is to present their proof.