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Details of Grant 

EPSRC Reference: GR/R82975/01
Title: Local Methods in Arithmetic Geometry
Principal Investigator: Flynn, Professor EV
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematical Sciences
Organisation: University of Liverpool
Scheme: Standard Research (Pre-FEC)
Starts: 16 September 2002 Ends: 15 September 2005 Value (£): 128,308
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
Arithmetic Geometry is a blend of Algebraic Geometry and Number Theory, two of the oldest branches of Mathematics in existence, with many centuries of history. Local methods for solving problems in Arithmetic Geometry are a long established part of the area, and have applications to virtually every branch of Mathematics from Algebra through to Mathematical Physics and Computer Security. Many of the fundamental problems in the area can be expressed as questions about local methods, and in particular obstructions to local methods. It is intended to concentrate on curves and surfaces, and to gain insight as to the range of obstructions that can occur.The proposed research will address questions about objects of central importance to Number Theorists, such as the Tate-Shafarevich group and the Manin obstruction. The proposal contains a wide range of levels of difficulties: some of the proposed work involves improving existing techniques, some involves the construction of examples which highlight desired properties (this is a portion of the research designed to be particularly accessible to the Research Associate), and some involves using this body of evidence to develop new theory and conjecture.
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Organisation Website: http://www.liv.ac.uk