Hiromu Tanaka
On Mori fibre spaces in positive characteristic.
The minimal model program conjecture predicts that any algebraic
variety is birational to either a minimal model or a Mori fibre
space. In this talk, we first summarise some results on Mori fibre
spaces in characteristic zero. We then discuss which properties
should extend to positive characteristic.
Gebhard Martin
Automorphism schemes of projective surfaces.
Given a proper variety X over a field k, its automorphism functor AutX is representable by a group
scheme locally of finite type over k. While the abstract
automorphism group AutX(k)
has always been an object of interest in classical algebraic
geometry, the automorphism scheme AutX
itself is usually not well-studied in positive characteristic, where
it contains more information than AutX(k).
However, the scheme structure of AutX
is of fundamental importance in the moduli and deformation theory of
X. In this talk, I will describe techniques that can be used to
determine AutX, give an
overview of what is known about AutX
if X is a (smooth) projective surface, and report on recent results
on automorphism schemes of projective surfaces of special type, such
as del Pezzo surfaces, elliptic surfaces, and surfaces of Kodaira
dimension 0.
Jakub Witaszek
Global ±-regularity and the Minimal Model Program for arithmetic
threefolds.
In this talk, I will explain a mixed characteristic analogue of
Frobenius regularity and how it can be used to establish the Minimal
Model Program for threefolds in mixed characteristic. This is based
on a joint work with Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi,
Karl Schwede, Kevin Tucker, and Joe Waldron.
Sergey Rybakov
Algebraic varieties over function fields and good towers of
curves over finite fields.
Given a smooth algebraic variety over a function field we can
construct a tower of algebraic curves (or, equivalently, a tower of
function fields). We say that the tower is good if the limit of the
number of points on a curve divided by genus is positive. For
example, the generic fiber of the Legendre family of elliptic curves
gives a good (and optimal) tower over Fp2.
I will speak on good towers coming from K3 surfaces.
File translated from TEX
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