SPGSV

Some Problems in Geometry of Shimura Varieties

Coordinatore	UNIVERSITY COLLEGE LONDON    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	United Kingdom [UK]
Totale costo	697˙037 €
EC contributo	697˙037 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2012-StG_20111012
Funding Scheme	ERC-SG
Anno di inizio	2012
Periodo (anno-mese-giorno)	2012-10-01   -   2017-09-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITY COLLEGE LONDON  Organization address address: GOWER STREET city: LONDON postcode: WC1E 6BT contact info Titolo: Dr. Nome: Andrei Cognome: Yafaev Email: send email Telefono: +44 20 7679 2861	UK (LONDON)	hostInstitution	697˙037.00
2	UNIVERSITY COLLEGE LONDON  Organization address address: GOWER STREET city: LONDON postcode: WC1E 6BT contact info Titolo: Mr. Nome: Giles Cognome: Machell Email: send email Telefono: +44 20 3108 3020 Fax: +44 20 7816 2849	UK (LONDON)	hostInstitution	697˙037.00

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 Obiettivo del progetto (Objective)

'The Andre-Oort conjecture is an important problem in the theory of Shimura varieties. It also has significant applications in other areas of Number Theory, such as transcendence theory. The conjecture was proved assuming the Generalised Riemann Hypothesis by Klingler, Ullmo and Yafaev. Very recently, Jonathan Pila came up with a very promising strategy for proving the Andre-Oort conjecture unconditionally. The first main aim of this proposal is to combine Pila's ideas with the ideas of Klingler-Ullmo-Yafaev in order to obtain a proof of the Andre-Oort conjecture without the assumption of the GRH. We then propose to use these methods to attack the Zilber-Pink conjecture, a very vast generalisation of Andre-Oort. We also propose to consider several problems closely related to geometry of Shimura Varieties and the Andr'e-Oort conjecture. Namely Coleman's cponjecture on finiteness of the number of Jacobians with complex multiplication for curves of large genus, the Mumford-Tate conjecture on Galois representations attached to abelian varieties over number field and Lang's conjecture on rational points on hyperbolic varieties in the context of Shimura varieties.'