Math 299 - p-adic Lie groups II

Course description: This is a continuation of p-adic Lie groups I (offered Winter 2015), which dealt with Part A of Schneider's book. We will go through Part B, on the algebraic theory of p-adic Lie groups. First we will give a detailed introduction to completed group rings ("Iwasawa algebras") of profinite groups. Then we will move on to Lazard's notion of a p-valuation on a group G, and study the Lie algebra gr(G) over F_p[P]. We will then discuss in detail the ring filtration on the Iwasawa algebra, and relate the graded algebra to U(gr(G)), following Lazard. At the end we will use this to show Iwasawa algebras are noetherian, and regular of finite global dimension. Depending on the number of active participants, each participant should expect to give ~4 talks. Let me know if you want to be added to the mailing list.

Instructor: Claus Sorensen, csorensen [at] ucsd [etcetera].

Meetings: Mondays 2-3, and Thursdays 1-2, in APM B412. (First meeting Apr 2nd.)

Textbook: Primarily p-Adic Lie Groups (Springer, 2011) by Peter Schneider, available here.

The original, Lazard.

If there's time, Schneider-Teitelbaum.

Prerequisites: Useful: p-adic analysis and p-adic Lie groups, as in Part A. However, for the most part, Part B is independent of Part A.