Mathematical Sciences: The Integral Hecke Structure of      Shimura Curves
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This research concerns the Shimura curve associated to an                  indefinite rational quaternion division algebra.  The rational                  structure of these curves have been understood for a long time,                 however there are many important questions to be answered                       concerning their integral structure.  Drinfeld gave the                         description as a course moduli scheme and this research will                    investigate their Hecke structure.                                                   This research is in one of the most erudite areas of                       arithmetic algebraic geometry, that subject which blends                        algebraic and geometric (and in this case analytic) techniques to               answer questions in number theory.  This research has already                   been a crucial ingredient in solving one of the big problems                    settled this year and will continue in the same direction during                the tenure of this award.  Much of great interest will be                       accomplished.
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{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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