Mathematical Sciences: Presidential Young Investigator
{'Code': '03040104', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
This research is primarily concerned with arithmetic on                    elliptic curves with complex multiplication, especially questions               related to the Birch and Swinnerton-Dyer conjecture, Iwasawa                    theory and p-adic L-functions.  Three specific problems are                     mentioned.  The first is to show that the invariant Sha is finite               and to give evidence for its conjectured order.  The second is to               study the p-adic analogues of the Birch and Swinnerton-Dyer                     conjecture.  The third is to determine certain special units in                 abelian extensions of fields of complex multiplication since                    these would very likely enable one to extend the earlier results                to higher dimensional abelian varieties with complex                            multiplication.
{'FirstName': 'Karl', 'LastName': 'Rubin', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Karl C Rubin', 'EmailAddress': 'krubin@math.uci.edu', 'NSF_ID': '000476610', 'StartDate': '08/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Ohio State University Research Foundation -DO NOT USE', 'CityName': 'Columbus', 'ZipCode': '432101016', 'PhoneNumber': '6146888734', 'StreetAddress': '1960 KENNY RD', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Ohio', 'StateCode': 'OH', 'CONGRESSDISTRICT': '03', 'CONGRESS_DISTRICT_ORG': 'OH03', 'ORG_UEI_NUM': 'QR7NH79713E5', 'ORG_LGL_BUS_NAME': None, 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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