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An arithmetic enrichment of the degree of a finite map, and applications to enumerative geometry

Derived algebraic geometry and its applications March 25, 2019 - March 29, 2019

March 26, 2019 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Kirsten Wickelgren (Georgia Institute of Technology)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • A^1 homotopy theory

  • enumerative geometry

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Abstract

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.

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