Cel 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. Dziedzina nauki natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometrysocial scienceslaw Program(-y) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Temat(-y) ERC-CoG-2015 - ERC Consolidator Grant Zaproszenie do składania wniosków ERC-2015-CoG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-COG - Consolidator Grant Instytucja przyjmująca TECHNISCHE UNIVERSITAET MUENCHEN Wkład UE netto € 1 328 710,00 Adres Arcisstrasse 21 80333 Muenchen Niemcy Zobacz na mapie Region Bayern Oberbayern München, Kreisfreie Stadt Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 1 328 710,00 Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE netto Rozwiń wszystko Zwiń wszystko TECHNISCHE UNIVERSITAET MUENCHEN Niemcy Wkład UE netto € 1 328 710,00 Adres Arcisstrasse 21 80333 Muenchen Zobacz na mapie Region Bayern Oberbayern München, Kreisfreie Stadt Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 1 328 710,00
