Algebraic Geometry Group

Members

Professors : Antoine Chambert-Loir, Laurent Moret-Bailly, Christophe Mourougane, 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 Étesse, Michel Gros.

PhD students : Davide Alessio, Damian Brotbek, Viviana Delanoy, Julien Dhondt, Mathilde Herblot, Kodjo Egadédé Kpognon, Jérémy Le Borgne, Cécile Le Rudulier, Charles Savel, Tristan Vaccon.

Some former members;: Noël Le Du, Ahmed Abbes, Anne Virrion, Pascal Autissier, Gweltaz Chatel, Daniel Conduché, João Pedro Dos Santos, Daniel Ferrand, Rodolphe Richard, Jérôme Poineau, Yichao Tian.

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 and mixed motives;
motivic integration and its relation with birational geometry.

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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.

2012, June 18–22 (Rennes): Pencils, formulas and stacks. an arithmetic geometry conference in the honour of Laurent Moret-Bailly.

Publications

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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