Date of Award

Spring 1-1-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Jonathan Wise

Second Advisor

Renzo Cavallieri

Third Advisor

Nathaniel Thiem

Fourth Advisor

David Grant

Fifth Advisor

Sebastian Casalaina-Martin

Abstract

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.

Included in

Mathematics Commons

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