Arithmetic Geometry and Number Theory RTG Seminar: An arithmetic enrichment of the degree of a finite map, and applications to enumerative geometry
Seminar | January 28 | 3-5 p.m. | 748 Evans Hall
Kirsten Wickelgren, Georgia Tech
Using the Eisenbud–Khimshiashvili–Levine local degree, which is the A1-local degree of Morel in A1-homotopy theory, we define a degree of a finite map between smooth schemes over k. When the target is appropriately connected, this degree is a bilinear form over k. We discuss some applications to enumerative geometry over non-algebraically closed fields. This is joint work with Jesse Kass and Jake Solomon, and will also contain joint work with Padmavathi Srinivasan.