Up to a finite covering, a sequence of nested subvarieties of an affine algebraic variety just looks like a flag of vector spaces (Noether); understanding this "up to" is a primary motivation for a fine study of finite coverings.
The aim of this talk is to give a bird's-eye view of some fundamental questions about them, which took root in Algebraic Geometry (descent problems etc.), then motivated major trends in Commutative Algebra (F-singularities etc.), and recently found complete solutions using p-adic methods (perfectoids). Rather than going into detail of the latter, the emphasis will be on synthesizing, from the geometric viewpoint, a rather scattered theme.
This is based on joint work with Luisa Fiorot.
You must be logged in to post a comment.