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Algebra Seminar

Monday, April 19, 2021 - 3:15pm

Thomas Brazelton

University of Pennsylvania


University of Pennsylvania


The A1-Brouwer degree, first constructed by Morel, provides a notion of local and global degrees for varieties, valued in the Grothendieck—Witt ring of the ground field. This is a crucial construction in motivic homotopy theory, and has also found fascinating applications in enriched enumerative geometry, where the Brouwer degree allows one to compute Grothendieck—Witt-valued Euler classes under certain hypotheses. In this talk, I will discuss recent work, joint with Stephen McKean and Sabrina Pauli, which demonstrates that local and global degrees can be computed using a multivariate Bézoutian. This result provides techniques and code for computing A1-degrees, and removes existing constraints about residue fields of points. As an application, we develop a toolkit of calculation rules satisfied by local and global degrees.