Algebraic Geometry Group

Members

Head : Julien Sebag.

Professor Emeritus : Pierre Berthelot, Laurent Moret-Bailly.

Professors : Christophe Mourougane, Matthieu Romagny, Julien Sebag.

Associate professors : Michele Bolognesi, David Bourqui, Lionel Fourquaux, Yongquan Hu, Florian Ivorra, Bernard Le Stum.

CNRS research associates (chargés de recherches) : Xavier Caruso, François Charles, Jean-Yves �tesse, Michel Gros.

PhD students : Julien Dhondt, Kodjo Egadédé Kpognon, Jérémy Le Borgne, Cécile Le Rudulier, Charles Savel, Tristan Vaccon.

General presentation

The research topics of the group cover the following themes:

• study of algebraic, rational or integral points of some algebraic varieties, in particular their height and their distribution; applications to arithmetical dynamical systems. The ideas and the techniques of Arakelov geometry play an important rôle;
• geometric questions, related to moduli problems (foundation of the theory of algebraic stacks, covers of curves, torsors) and their arithmetical applications;
• development of cohomological methods used in arithmetic geometry: étale cohomology, p-adic cohomologies (crystalline and rigid), extension of the theory of modules over rings of differential operators (D-modules) outside characteristic zero;
• development of arithmetic structures related to p-adic Hodge theory;
• motivic cohomology, mixed motives and motivic integration.

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Activities

The group organizes a weekly seminar on various topics going from algebraic geometry and topology to number theory (organizer: Yongquan Hu) which takes place on Thursdays, from 10:30 to 11:30.

The Geometry Seminar is run jointly by the three IRMAR geometry groups (organizer: Michele Bolognesi).

The group also takes part in the organization of the weekly cryptography seminar.

Conferences organized by members of the team

Upcoming events :

thematic semester 2014 (Labex H. Lebesgue) ;

final conference ANR CETHop (April 22-26 2013 CIRM Luminy).

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Networks

Some members of the group are part of the GDR 3064 Géométrie algébrique complexe.

Some members of the group take part in various projets of the Agence nationale de la recherche :

• Positive (Positivity in algebraic, arithmetic and analytic geometry) ;
• Aspects algébrique et analytique de la géométrie complexe en dimension supérieure
• Applications de la géométrie de Berkovich.
• Calculs effectifs en théorie de Hodge p-adique (CETHop)
• Points entiers et points rationnels.

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