Given a finite morphism of smooth curves, the Prym variety parametrizes line bundles on the source whose norm is isomorphic to the canonical bundle of the target. What if the target and/or the source are not smooth? Several people already…

# Categoria evento: Algebraic and Arithmetic Geometry Seminar

## Algebraic classes in mixed characteristic and André’s p-adic periods – Giuseppe Ancona (Université de Strasbourg)

(Joint work with D. Fratila) Motivated by the study of algebraic classes in mixed characteristic, we define a countable subalgebra of ${\Bbb Q}_p$ which we call the algebra of “Andre’s p-adic periods”. We will explain the analogy and the difference…

## Lafforgue variety and $p$-adic representations – Kostas I. Psaromiligkos (University of Chicago)

We will construct the Lafforgue variety, a parametrizing space for the smooth irreducible representations of a $p$-adic reductive group $G(F)$. Our main tools will be Hecke algebras and a noncommutative version of the Hilbert scheme. The Lafforgue…

## On reduction steps for Leopoldt’s conjecture – Fabio Ferri (Università di Exeter)

Let $p$ be a rational prime and let $L/K$ be a Galois extension of number fields with Galois group $G$. Under some hypotheses, we show that Leopoldt’s conjecture at $p$ for certain proper intermediate fields of $L/K$ implies Leopoldt’s conjecture at…

## The Complexity of Higher Chow Groups – James Lewis (University of Alberta)

Let $X/{\mathbb C}$ be a smooth projective variety. We consider two integral invariants, one of which is the level of the Hodge cohomology algebra $H^*(X,{\mathbb C})$ and the other involving the complexity of the higher Chow groups ${\rm…

## A family of threefolds with remarkable properties (namely: the unreasonable effectiveness of the Schoens) – Antonella Grassi (Università degli Studi di Bologna)

The fiber product of certain rational elliptic surfaces were first studied by Schoen in the 80s to answer questions from string theory. Over the decades the “Schoens” have provided evidence for various conjectures as well as counterexamples to…

## Quot schemes and their d-critical structure(s) – Andrea Ricolfi (SISSA, Trieste)

D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical…

## Incontri di geometria algebrica ed aritmetica Milano – Pisa

Schedule available on: https://events.dm.unipi.it/event/109/…

## Arithmetic of homogeneous spaces over global fields of characteristic p – David Harari (Université de Paris-Saclay)

Let $K$ be the function field of a curve over a finite field. Let $X$ be a homogeneous space of a reductive group over $K$. We discuss cohomological obstructions to the local-global principle on $X$. Similar results for weak and strong approximation…

## Hilbert-Kunz density function and its applications to some Hilbert-Kunz multiplicity conjectures – Vijaylaxmi Trivedi (Tata Institute of Fundamental Research, India)

In this talk we introduce a compactly supported and real valued continuous function called Hilbert-Kunz (HK) density function. We briefly describe its properties and its applications to study characteristic p-invariants like HK multiplicity and F…