时间：2026年4月21日（周二）14:00-16:00
地点：E14-301
主讲人：Gerard Freixas, École Polytechnique
讲座主题：On the Deligne–Riemann–Roch Isomorphism
讲座摘要：In algebraic geometry, the Grothendieck-Riemann-Roch formula describes the functoriality of the Chern character under pushforward. In 1985, in a letter to Quillen, Deligne conjectured that the degree-one part of this formula is the shadow of a more precise statement, namely a canonical isomorphism between line bundles. This isomorphism is expected to express the Knudsen–Mumford determinant of cohomology in terms of a construction akin to an "intersection theory with values in line bundles," and to enjoy good functorial properties.
At the time, several special cases of this phenomenon were known. These include the theory of the different and discriminants, the functional equation of the Riemann theta function, certain very specific instances of Poincaré duality, and Mumford’s isomorphism for pluricanonical forms on curves. Deligne established his conjecture in the case of families of curves, using Mumford's isomorphism. Later, Elkik developed part of the theory of intersection with values in line bundles.
Recently, in joint work with Dennis Eriksson, we completed Elkik's work and constructed the isomorphism predicted by Deligne. In this talk, I will motivate the problem along the lines described above, and present our result with Dennis, together with some of its consequences.
