Back to Commutative Algebra Seminar: Fall 2019
Commutative Algebra Seminar
Date: Friday, Nov 1, 2019
Time: 3:30PM - 4:30PM
Location: LCB 225
Stephen H. McKean
Duke University
Title |
Enriching Bézout’s Theorem |
Abstract |
Classically, Bézout’s Theorem counts the number of intersections of two generic algebraic curves over an algebraically closed field. Using tools from A^1-homotopy theory and building on the work of Jesse Kass and Kirsten Wickelgren, we give an enrichment of Bézout’s Theorem over any perfect field. Over algebraically closed fields, this enrichment recovers the classical version of the theorem. Over non-algebraically closed fields, this enrichment imposes a relation on the tangent directions of the curves at their intersection points. As concrete examples, we will discuss Bézout’s Theorem over the reals and finite fields. |
Commutative Algebra