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Seminario Matematico e Fisico di Milano
Kestutis Cesnavicius
Institut de Mathématique d'Orsay, Université Paris-Saclay
The perfectoid approach to purity questions

Lunedì 15 Novembre 2021, ore 16:00
Sala di Rappresentanza, Via C. Saldini 50, Milano e ON LINE
Abstract
Purity in arithmetic algebraic geometry is the phenomenon of certain invariants of algebraic varieties being insensitive to removing closed subvarieties of sufficiently large codimension, the Hartogs' extension principle being the basic example. The most delicate case of such results is in mixed characteristic (0, p), in which a new approach based on perfectoid rings has recently been introduced. I will overview it and discuss the results that it has yielded so far.