Formal groups and lifts of the field of norms
Time: Mon, 18 Nov 2019, 15:30-17:00
Place: Lecture hall at the 3rd floor, Jinchunyuan West Building
Speaker: Léo Poyeton (BICMR, Peking University)
Abstract:
Let K be a finite extension of ℚp. A useful tool to study p-adic representations of GK = Gal(K̅/K) is the theory of cyclotomic (φ,Γ)-modules of Fontaine, which relies on a characteristic 0 lift of the field of norms of the cyclotomic extension. In this talk, we will be interested in the following question: by what kind of Galois extensions K∞/K can we replace the cyclotomic extension in order to build a (φ,Γ)-modules theory? We will show that under a certain additional assumption, such an extension is generated by the torsion points of a relative Lubin-Tate group and that the power series giving the action of the Galois group of K∞/K are twists of semi-conjugates of endomorphisms of the same relative Lubin-Tate group.