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…
Categoria evento: Algebraic and Arithmetic Geometry Seminar
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…
On finite presentation for the tame fundamental group – Vasudevan Srinivas (Tata Institute of Fundamental Research, India)
This is a report on joint work with H. Esnault and M. Schusterman.Recall that the étale fundamental group of a variety over an algebraically closed field of characteristic 0 is known to be a finitely presented profinite group; this is proved by…
The Heisenberg category of a category – Ádám Gyenge (Alfréd Rényi Institute of Mathematics)
The Heisenberg algebra associated with a lattice is a much-investigated object originating in quantum theory. Khovanov introducedrecently a categorification of the infinite Heisenberg algebraassociated with the free boson or, equivalently, a rank 1…
Hecke correspondences and Lagrangian fibrations – Sam DeHority (Columbia University)
I will discuss a method to associate new algebraic structures with deformations to certain holomorphic Lagrangian fibrations, and describe their relation with other parts of mathematical physics. This algebraic structure controls the enumerative…