Séminaire de Géométrie Tropicale
Mercredi 20 avril 2016 14h salle 1525-502
Andrew Macpherson
(IHES)
A categorical approach to non-Archimedean geometry
Résumé :
I outline an approach to defining non-Archimedean geometry in terms of categories of modules, in a programme broadly similar to Toën-Vaquié's relative algebraic geometry. This work differs from previous attemps to do the same thing in that it defines the necessary topological rings and modules 'from scratch', in the purely categorical language of ind-pro-objects. One advantage this offers is that it easily provides reasonable notions of finitely presented quasi-coherent sheaves and of flatness without any absolute finiteness hypotheses.