Motives and Complex multiplication

14-19 août 2016

Prof. Jossen Peter, ETHZ Dr. Javier Fresán, ETHZ Prof. Richard Pink, ETHZ

Ben Moonen, Nijmegen Fabrizio Andreatta, Milano Frans Oort, Utrecht Giuseppe Ancona, Essen Damian Rössler, Toulouse Lenny Taelman, Leiden Jakob Tsimerman, Toronto Maryna Viazovska, Humboldt U. Berlin Jörg Wildeshaus, Paris 13 Masanori Asakura, Hokkaido

In this summer school, intended for Ph.D. students and early stage researchers, we bring together Motives and the much older theory of Complex Multiplication. Since their introduction about 50 Years ago by Alexander Grothendieck, motives have become an essential tool in studying arithmetic and geometric properties of algebraic varieties. A motive with complex multiplication is a motive that has, in a precise sense, many endomorphisms. For example, the cohomology of an abelian variety of CM-type is a motive with complex multiplication. These extra endomorphisms make it easier to study objects which are classically associated with motives in general. For instance, the periods of a motive with complex multiplication are beautifully related to special values of the Gamma function. The notion of motives with complex multiplication also rises intriguing problems. For example, whenever motives appear in an algebraic family one wishes to understand the set of parameters at which the motive in the family has complex multiplication. Concretely we can ask: How many algebraic curves in a family have a Jacobian which is an abelian variety of CM-type? In this summer school, experts of international standing will present history and state-of-the-art of results and questions around motives and complex multiplication. Mini Courses: Ben Moonen, Nijmegen, (Around the Mumford-Tate conjecture) Fabrizio Andreatta, Milano, (Special cycles on Shimura varieties) Oort, Frans, Utrecht (Lecture series on CM Jacobians) Lectures: Giuseppe Ancona, Essen, (Chow--Künneth Decompositions) Damian Rössler, Toulouse, (CM motives in Arakelov Geometry) Lenny Taelman, Leiden, (TBA) Jakob Tsimerman, Toronto, (Around the André Oort Conjecture) Maryna Viazovska, Humboldt, (Special values of Green's function) Jörg Wildeshaus, Paris 13, (Boundary motives) Masanori Asakura, Hokkaido, (CM periods and regulators)

Monte Verita

55