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Algebra Seminar

Friday, November 5, 2021 - 3:30pm

Thomas Brazelton

University of Pennsylvania


University of Pennsylvania


Given any local or global complete intersection over a field, one can provide an associated residue form, which is a bilinear form encoding algebrao-geometric data. In recent years, these forms have provided a way to compute Brouwer degrees for maps of varieties in motivic homotopy theory, providing a powerful computation tool for determining, among other things, solutions to enumerative geometry problems over other fields. We will present on recent work with Stephen McKean which discusses how residue forms interact with base change to inseparable extensions in the univariate setting. Namely, we demonstrate that there are suitable lifts of polynomials at closed points, whose residue forms can be traced down from Grothendieck—Witt rings along transfers arising from stable motivic homotopy theory. Moreover we demonstrate that scaled trace forms, as in number theory, are local Brouwer degrees of univariate maps.