Mathematical Sciences: Higher Regulators, Algebraic Cycles, and Values of L-functions
{'Code': '03040300', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle'}
This research will continue the investigations of the P.I.                 on the structure of cycles and K-theory of arithmetic varieties                 and their (conjectural) relationship to values of L-functions at                integral points.  He will analyze certain selected conjectures of               Beilinson, Bloch and Tate in the context of modular varieties                   where one can use the theory of automorphic forms.                                   This research is in the blend of topics encompassing number                theory, algebraic geometry and automorphic forms.  That is, it                  brings to bear tools from algebra, analysis and geometry to                     analyze number theoretic problems.  The "values of L-functions"                 give analytic expression to explicit numbers of great arithmetic                significance allowing for their deeper study.  The P.I. has                     contributed many interests results to this area in the past and                 will surely do so further during this research.
{'FirstName': 'Dinakar', 'LastName': 'Ramakrishnan', 'EmailAddress': 'dinakar@its.caltech.edu', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Cornell University', 'CityName': 'Ithaca', 'ZipCode': '148502820', 'PhoneNumber': '6072555014', 'StreetAddress': '373 Pine Tree Road', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY'}
{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703602.xml'}