Details of Grant 

EPSRC Reference:	GR/R29994/01
Title:	Rational Points and the Hasse Principle
Principal Investigator:	Skorobogatov, Professor A
Other Investigators:
Researcher Co-Investigators:
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Department:	Mathematics
Organisation:	Imperial College London
Scheme:	Standard Research (Pre-FEC)
Starts:	01 October 2001	Ends:	30 September 2003	Value (£):	80,826
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Summary on Grant Application Form
The main purpose is to understand the behaviour of rational points on algebraic varieties over number fields, mostly in connection with the Hasse principle and weak approximation. We intend to study the interrelations of the obstructions to the Hasse principle, such the Manin obstruction and the non-abelian descent obstruction, with other known techniques, such as decent, torsors, fibration methods, Swinnerton-Dyer's recent method of variation of Selmer groups in a pencil of elliptic curves. We hope to get a more sysematic picture of the phenomena related to the Hasse principle on different types of algebraic varieties. Even partial progress in these directions will substantially increase our understanding of rational points, and is likely to lead to strong number-theoretic results.
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Organisation Website:	http://www.imperial.ac.uk