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# Séminaire Géométrie Ergodique

Salle de conférences – Centre de Mathématiques Laurent Schwartz

10h30-12h30 – Florent Martin (Ratisbone)

"Differentiability of non-archimedean volumes"

Abstract: Let K be a discretely valued non-archimedean field, X a projective variety over K and L a line bundle on X equipped with a continuous metric. Following Kontsevich and Tschinkel, we introduce a notion of  non-archimedean volume which measures the asymptotic volume of the set of small sections of powers of L. The result I want to explain is that this volume satisfies a differentiability property if the metric is semipositive, and the derivative is given by integration with respect to the associated Chambert-Loir measure. As an application, one can remove an algebraicity assumption in the work of Boucksom, Favre and Jonsson on the non-archimedean Monge-Ampère problem. This is a joint work with J. Burgos, W. Gubler, P. Jell and K. Künnemann.

14h30-15h30 – Shou-Wu Zhang (Princeton, IHES)

"Admissible height pairing of algebraic cycles"