Seminar Announcement

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT

Speaker: Alessandro Maria Masullo, Stanford

Title: Perfectoid spaces and their applications

Abstract: I will give a fairly detailed and at the same time
motivational view on the theory of Perfectoid Spaces, introduced by
Peter Scholze a few years ago, building on some explicit examples. I'm
going to briefly sketch the main deep ideas which led to the birth of
Perfectoid Spaces, mainly due to Tate, Faltings and Fontaine. Once
introduced the notion of an affinoid perfectoid space, avoiding few
technicalities, I will state the main deep theorems which, roughly,
explain how Perfectoid Spaces serve as a bridge between the
mixed-characteristic (0,p) world, p a prime, and the characteristic p
world, in terms of spaces and their étale cohomology. I will
explicitly solve an instructive exercise proving that every connected
affinoid Noetherian rigid space over Q_p is a K(pi, 1),, which will
only need the basics, and will at once show the power of the theory.
Time permitting, I will sketch one more advanced topic leading to
results of mine which are intended to "geometrize" Iwasawa Theory by
means of the natural geometric framework provided by adic spaces and
their "perfectoid covers".
Lecture notes will be provided shortly after the seminar.

Venue: SISSA, lecture room 136, Friday 25 September at 11:00