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arXiv · 1906.00921

Automorphisms of categories of schemes

Remy van Dobben de Bruyn
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Abstract

Given two schemes $S$ and $S'$, we prove that every equivalence between $\mathbf{Sch}_S$ and $\mathbf{Sch}_{S'}$ comes from a unique isomorphism between $S$ and $S'$. 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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Remy van Dobben de Bruyn. 2019-06-03. Automorphisms of categories of schemes. https://arxiv.org/abs/1906.00921

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