U.S.-France Cooperative Research: Arakelov Geometry and itsApplications

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This award will support collaborative research in algebra and number theory between Dr. Henri Gillet, University of Illinois at Chicago, and Dr. Christian Soule, Director of Research at the French National Center for Scientific Research and presently at the Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France. Drs. Gillet and Soule propose to investigate the relationship between analytic and algebraic constructions which occur in arithmetic geometry. In particular they will pursue the applications of their previous work on arithmetic intersection theory and the arithmetic Riemann-Roch theorem to problems in geometry and number theory. Specific areas to be studied include the inequalities in Arakelov geometry, the Adelic Arakelov theory. Dr. Gillet is one of the leading experts on the relationships between K-theory and algebraic geometry, as well as on the Arakelov theory. This award will allow him to continue a highly fruitful collaboration with an outstanding French mathematician with complementary expertise.