Combinatorics and Arithmetic for Physics: special days

Collection Combinatorics and Arithmetic for Physics: special days

Organizer(s) Gérard H.E. Duchamp, Maxim Kontsevich, Gleb Koshevoy et Vincel Hoang Ngoc Minh
Date(s) 30/11/2021 - 02/12/2021
linked URL
00:00:00 / 00:00:00
9 20

A Functorial Excursion between Algebraic Geometry and Linear Logic

By Paul-André Melliès

In this talk, I will use the functor of points approach to Algebraic Geometry to establish that every covariant presheaf X on the category of commutative rings — and in particular every scheme X — comes equipped “above it” with a symmetric monoidal closed category PshModX of presheaves of modules. This category PshModX defines moreover a model of intuitionistic linear logic, whose exponential modality is obtained by glueing together in an appropriate way the Sweedler dual construction on ring algebras. The purpose of this work is to explore the idea that linear logic is a logic of generalised vector bundles, in the same way as dependent type theory is understood today as a logic of spaces up to homotopy.

Information about the video

Last related questions on MathOverflow

You have to connect your account with mathoverflow to add question

Ask a question on MathOverflow


  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
  • Get notification updates
    for your favorite subjects
Give feedback