## Non-archimedean Monge-Ampère equations

### Mardi 9 janvier 2018 14:15-15:15 - Walter Gubler - Universität Regensburg

Résumé : We study non-archimedean volumes, a tool which allows us to control the asymptotic
growth of small sections of big powers of a metrized line bundle. We prove that the nonarchimedean volume is differentiable at a continuous semipositive metric and that the derivative is given by integration with respect to a Monge-Ampere measure. Such a differentiability formula had been proposed by M. Kontsevich and Y. Tschinkel. In residue characteristic zero, it implies an orthogonality property for non-archimedean plurisubharmonic functions which allows us to drop an algebraicity assumption in a theorem of S. Boucksom, C. Favre and M. Jonsson about the solution to the non-archimedean Monge-Ampere equation. We will also present a similar result in positive equicharacteristic assuming resolution of singularities.

Lieu : IMO Bât. 307, salle 3L15

Non-archimedean Monge-Ampère equations  Version PDF
novembre 2019 :
 Département de Mathématiques Bâtiment 307 Faculté des Sciences d'Orsay Université Paris-Sud F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 Département Fermeture du département Laboratoire Formation