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

该奖项将支持芝加哥伊利诺伊大学Henri Gillet博士和法国国家科学研究中心主任Christian Soule博士在代数和数论方面的合作研究，Christian Soule博士目前在布尔斯-苏维特高等科学研究所工作。法国。Drs。Gillet和Soule提议研究算术几何中出现的解析结构和代数结构之间的关系。特别是，他们将继续研究算术交点理论和算术黎曼-洛克定理在几何和数论问题上的应用。要研究的具体领域包括阿拉克洛夫几何中的不等式，阿德利克·阿拉克洛夫理论。Gillet博士是研究k理论与代数几何关系以及Arakelov理论的主要专家之一。该奖项将使他能够继续与一位具有互补专长的杰出法国数学家进行卓有成效的合作。

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.