Automorphisms of categories of schemes
Remy van Dobben de Bruyn
TL;DR
This paper proves that any categorical equivalence between schemes over different bases arises from a unique isomorphism of those bases, removing previous restrictions and fully resolving a longstanding mathematical question.
Contribution
It establishes a complete characterization of equivalences between categories of schemes, showing they are induced by base isomorphisms without Noetherian or finite type assumptions.
Findings
Equivalence of scheme categories implies base scheme isomorphism.
Removes Noetherian and finite type restrictions from previous results.
Answers a question posed by Brandenburg in 2011.
Abstract
Given two schemes and , we prove that every equivalence between and comes from a unique isomorphism between and . This eliminates all Noetherian and finite type hypotheses from a result of Mochizuki and fully answers a programme set out by Brandenburg in a series of questions on MathOverflow in 2011.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
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