Mathematical Sciences: Syzygies and Algebraic Groups
{'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 project is concerned with several problems in                         commutative algera. The principal investigators will work on the                Horrocks'conjecture. They will also work on the syzygy theorem                  and extending certain results to the mixed characteristic case.                 Another area of concentration concerns invariants related to                    representations of groups in positive characteristic. One of the                main problems to be considered in this area is to describe how                  tensor functors, acting on indecomposable representations,                      decompose.                                                                           The research in this project involves two areas of                         commutative algebra. The first area is concerned with the                       structure and properties of syzygies of finite projective                       dimension and uses local commutative algebra. A "syzygy" is a                   linking or yoking together of steps in a projective resolution                  describing the structure of a module. The second area is                        concerned with decomposing tensor functors under formal group                   laws and the properties of the relative Grothendieck groups that                are associated to the decomposition.
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{'Name': 'University of Illinois at Urbana-Champaign', 'CityName': 'URBANA', 'ZipCode': '618013620', 'PhoneNumber': '2173332187', 'StreetAddress': '506 S WRIGHT ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '13', 'CONGRESS_DISTRICT_ORG': 'IL13', 'ORG_UEI_NUM': 'Y8CWNJRCNN91', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ILLINOIS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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