Mathematical Sciences: A New Approach to Falting's Metrics  on Cohomology in Arakelov Theory
{'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 will concentrate on the ideas surrounding                    Faltings definition of certain volume forms on cohomology groups,               which were used in his proof of the Riemann-Roch theorem for                    Arakelov surfaces.  The Principal Investigator has discovered a                 new approach to these volume forms, obtaining them from certain                 metrics on the cohomology groups.  He has a rather direct                       geometric construction of these metrics which shows them to be in               analogy with the non-archimedean metrics induced at the finite                  places by the choice of a model.  He will apply this construction               to the study of Faltings' delta invariant for Riemann surfaces,                 to the definition and study of the non-archimedean analog of this               invariant , and to the study of Arakelov's zeta functions.                           This research is in the area of applying geometric methods                 to solve equations in integers (Diophantine equations).  Faltings               recent fundamental work in this area is the jumping off point for               the work of this researcher.
{'FirstName': 'William', 'LastName': 'McCallum', 'PI_MID_INIT': 'G', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'William G McCallum', 'EmailAddress': 'wmc@math.arizona.edu', 'NSF_ID': '000091431', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Arizona', 'CityName': 'TUCSON', 'ZipCode': '85721', 'PhoneNumber': '5206266000', 'StreetAddress': '845 N PARK AVE RM 538', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Arizona', 'StateCode': 'AZ', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'AZ07', 'ORG_UEI_NUM': 'ED44Y3W6P7B9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ARIZONA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8802779.xml'}