Morgan Opie

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20182025

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math.AT2019

The trace of the local $A^{1}$ -degree

Thomas Brazelton, Robert Burklund, Stephen McKean +2

We prove that the local $A^{1}$ -degree of a polynomial function at an isolated zero with finite separable residue field is given by the trace of the local $A^{1}$ -deg…

math.AT2018

Localization in Homotopy Type Theory

J. Daniel Christensen, Morgan Opie, Egbert Rijke +1

We study localization at a prime in homotopy type theory, using self maps of the circle. Our main result is that for a pointed, simply connected type $X$ , the natural map $X \to X_…

The trace of the local A1-degree

Localization in Homotopy Type Theory

The trace of the local $A^{1}$ -degree