Tuesday, January 16, 2018 - 13:15
Johann von Neumann-Haus, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, 3.006, Haus 3, Erdgeschoss
Forschungsseminar Arithmetische Geometrie
Prof. Jürg Kramer / Prof. Thomas Krämer
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-Ampère 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-Ampère equation. We will also present a similar result in positive equicharacteristic assuming resolution of singularities.
submitted by Marion Thomma (thomma@math.hu-berlin.de, 2093-5815)