Functional Analysis Over the Integers, L-Functions and Global Hodge Theory

Watch this conference talk from the Arithmetic Quantum Field Theory Conference where Oxford's Kobi Kremnitzer explores the development of functional analysis over integers through bornological methods, unifying Archimedean and non-Archimedean analysis. Discover how algebras of functions and distributions defined over integers can be base changed to conventional algebras over reals and p-adics, leading to the formulation of L-functions over integers. Learn about an innovative analytic stack over integers whose quasi-coherent sheaves category yields global Hodge structures, and understand the connection between integral L-functions and line bundle trivializations on this stack. Explore a new cohomology theory for schemes valued in global Hodge structures, potentially related to q-deRham, and consider theoretical connections between cohomology determinants and L-functions. The presentation covers collaborative work in progress with Federico Bambozzi and Jack Kelly.