Title: Functional analysis over the integers, L-functions and global Hodge theory
by
DrKobi Kremnitzer(University of Oxford)
→
Europe/Berlin
Description
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.