Obiettivo The proposed project concerns p-adic Hodge Theory, a major area of arithmetic algebraic geometry; it owes its existence to the 1968 observation of John Tate that the well-known Hodge decomposition of the singular cohomology of a complex manifold should have a p-adic analogue, in which the singular cohomology is replaced by the p-adic etale cohomology.There are currently two distinct approaches to the study of this Hodge-Tate decomposition. The first, developed mainly by Bloch, Kato, and Tsuji, uses algebraic K-theory, syntomic complexes, and p-adic vanishing cycles, while the second, more in line with Tate's original ideas, was developed by Faltings using his almost mathematics and purity theorems.The project will resolve a number of outstanding open problems in the field, including the relation between these distinct methods, the resolution of a 1983 conjecture of Bloch on vanishing cycles, and the development of integral results keeping track of p-torsion. It is a particularly timely moment to carry out such a project as the ER has recently developed a new integral p-adic cohomology theory with Bhatt and Scholze, while the Supervisor has recently put Faltings' machinery on a rigorous base in an extended joint work with Gros. The conjunction of the complementary backgrounds of the ER and Supervisor will be central to the project. Specifically, the ER's recent work with Bhatt and Scholze, as well as his expertise in K-theory, topological cyclic homology, de Rham--Witt methods, etc., will be merged with the Supervisor's detailed understanding of the aforementioned works of Bloch, Kato, Tsuji, and Faltings. The theories of perfectoid spaces and pro-etale cohomology, as introduced by Scholze, will play a fundamental role. Campo scientifico natural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Parole chiave p-adic Hodge theory vanishing cycles K-theory Programma(i) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Argomento(i) MSCA-IF-2015-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Invito a presentare proposte H2020-MSCA-IF-2015 Vedi altri progetti per questo bando Meccanismo di finanziamento MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Coordinatore INSTITUT DES HAUTES ETUDES SCIENTIFIQUES Contribution nette de l'UE € 173 076,00 Indirizzo ROUTE DE CHARTRES 35 91440 Bures Sur Yvette Francia Mostra sulla mappa PMI L’organizzazione si è definita una PMI (piccola e media impresa) al momento della firma dell’accordo di sovvenzione. Sì Regione Ile-de-France Ile-de-France Essonne Tipo di attività Research Organisations Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 173 076,00