100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Samuel Lerbet

The Serre–Swan correspondence.
Jeudi, 24 Novembre, 2022 - 17:00
Résumé : 

In his landmark 1955 paper Faisceaux algébriques cohérents, Serre proved that algebraic vector bundles on affine varieties are equivalent to finite projective modules on its coordinate ring. This led to the “folklore” that (real) topological vector bundles over a compact Hausdorff space X should be the same as finite projective modules on its “coordinate ring” which in the topological context is the ring of continuous functions from Xto R. It allowed geometers to provide examples of projective modules with interesting properties using corresponding features of topological vector bundles. This topological folklore was put on firm grounds by Swan in 1962 and this phenomenon of (vector bundle)-(finite projective modules) association is now dubbed the Serre–Swan correspondence. The talk aims to explain the main ideas of Swan's proof, which is entirely topological, and the application of the Serre–Swan correspondence to the construction of non-free finite projective modules.

Institution de l'orateur : 
Insitut Fourier
Thème de recherche : 
Salle : 
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