Radius of convergence of differential modules over valued rings: old and new
by
Gilles Christol
Université Paris 6

Let A be a valued ring endowed with a derivation D. For each A[D]-module, free of finite rank as A-module, we define a radius of convergence. This basic notion had several avatars: Katz's proof of Turritin theorem, Robba's Hensel lemma for differential operators, ... This radius of convergence is shown to be continuously depending on the valuation (in the sense of Berkovich). A generalisation in the several variables case (namely several commuting derivations) is now available (Baldassarri-Di Vizio).

Date received: June 7, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-57.