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University of Colorado

1. Willis, John Martin. Topological Foundations of Tropical Geometry.

Degree: PhD, 2019, University of Colorado

URL: https://scholar.colorado.edu/math_gradetds/70

We construct two subcanonical Grothendieck Topologies on the category of commutative, integral monoids and show that the moduli space of tropical curves is a stack in both topologies. We additionally construct two subcanonical topologies on the category of sharp, saturated, integral, commutative monoids with an eye towards answering outstanding questions of algebraicity of tropical moduli problems.
*Advisors/Committee Members: Jonathan Wise, Renzo Cavallieri, Nathaniel Thiem, David Grant, Sebastian Casalaina-Martin.*

Subjects/Keywords: algebraic geometry; monoids; topology; tropical geometry; Mathematics

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APA (6^{th} Edition):

Willis, J. M. (2019). Topological Foundations of Tropical Geometry. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/70

Chicago Manual of Style (16^{th} Edition):

Willis, John Martin. “Topological Foundations of Tropical Geometry.” 2019. Doctoral Dissertation, University of Colorado. Accessed October 28, 2020. https://scholar.colorado.edu/math_gradetds/70.

MLA Handbook (7^{th} Edition):

Willis, John Martin. “Topological Foundations of Tropical Geometry.” 2019. Web. 28 Oct 2020.

Vancouver:

Willis JM. Topological Foundations of Tropical Geometry. [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2020 Oct 28]. Available from: https://scholar.colorado.edu/math_gradetds/70.

Council of Science Editors:

Willis JM. Topological Foundations of Tropical Geometry. [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/math_gradetds/70