Title: Functional analysis over the integers, L-functions and global Hodge theory

by Dr Kobi Kremnitzer (University of Oxford)

Tuesday 25 Jun 2024, 05:00 → 06:00 Europe/Berlin

Abstract:

In this talk I will explain what are bornologies and how using bornological methods one can develop functional analysis 

over the integers unifying Archimedean and non-Archimedean analysis. I will give examples of algebras 

of functions and distributions defined over the integers which base change to the usual algebras over the reals and p-adics. 

Using these it is possible to write some version of L-functions over the integers. I will also discuss how this approach gives global analytic geometry and global Hodge structures. I will relate the integral L-functions to global Hodge structures. I will also explain how to define a cohomology theory for schemes valued in global Hodge structures and speculate 

on the relation between the determinant of cohomology and L-functions.