Adic Spaces I
We will recall the definition and some properties of Huber rings and we will define and study spaces of continuous valuations.
Adic Spaces II: Examples
We will explain in detail some examples of affinoid adic spaces including the unit ball (for rank 1 valuations). If time permits we will talk on completion and rational subsets.
Arithmetic Okounkov bodies I
We will review the construction of Newton-Okounkov bodies by Kaveh-Khovanskii and Lazarsfeld-Mustata, within a general framework of semigroups and cones associated to filtrations.
Arithmetic Okounkov bodies II
We will address the construction of arithmetic Newton-Okounkov bodies, and more generally functions on Newton-Okounkov bodies arising from filtrations, following ideas of Boucksom and collaborators.
Arithmetic Okounkov bodies III
In the third talk we will continue the discussion of arithmetic Newton-Okounkov bodies and more.
Perfectoid spaces I
Perfectoid spaces are specially interesting instances of adic spaces.
Positividad aritmética sobre variedades tóricas
Espais àdics feixistes
Estudiarem com definir un candidat a feix estructural per a un espai afinoide (de la forma Spa(A,A^+)) i en quins casos surt un feix.
What is…a Darmon point?
The theory of Heegner points, which form a supply of algebraic points on a given elliptic curve, are one of the main tools used in proving the known cases of the Birch and Swinnerton-Dyer conjecture.