Objectif Algebraic geometry deals with algebraic varieties, that is, systems of polynomial equations and their geometric interpretation. Its ultimate goal is the classification of all algebraic varieties. For a detailed understanding, one has to construct their moduli spaces, and eventually study them over the integers, that is, in the arithmetic situation. So far, the best results are available for curves and Abelian varieties.To go beyond the aforementioned classes, I want to study arithmetic moduli spaces of the only other classes that are currently within reach, namely, K3 surfaces, Enriques surfaces, and Hyperkähler varieties. I expect this study to lead to finer invariants, to new stratifications of moduli spaces, and to open new research areas in arithmetic algebraic geometry. Next, I propose a systematic study of supersingular varieties, which are the most mysterious class of varieties in positive characteristic. Again, a good theory is available only for Abelian varieties, but recently, I established a general framework via deformations controlled by formal group laws. I expect to extend this also to constructions in complex geometry, such as twistor space, which would link so far completely unrelated fields of research.I want to accompany these projects by developing a general theory of period maps and period domains for F-crystals, with an emphasis on the supersingular ones to start with. This will be the framework for Torelli theorems that translate the geometry and moduli of K3 surfaces, Enriques surfaces, and Hyperkähler varieties into explicit linear algebra problems, thereby establishing new tools in algebraic geometry. Champ scientifique natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometrysocial scienceslaw Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-CoG-2015 - ERC Consolidator Grant Appel à propositions ERC-2015-CoG Voir d’autres projets de cet appel Régime de financement ERC-COG - Consolidator Grant Institution d’accueil TECHNISCHE UNIVERSITAET MUENCHEN Contribution nette de l'UE € 1 328 710,00 Adresse Arcisstrasse 21 80333 Muenchen Allemagne Voir sur la carte Région Bayern Oberbayern München, Kreisfreie Stadt Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 328 710,00 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire TECHNISCHE UNIVERSITAET MUENCHEN Allemagne Contribution nette de l'UE € 1 328 710,00 Adresse Arcisstrasse 21 80333 Muenchen Voir sur la carte Région Bayern Oberbayern München, Kreisfreie Stadt Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 328 710,00
