# Automorphisms of categories of schemes

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Remy van Dobben de Bruyn, Princeton University
Fine Hall 401

We prove that any scheme S can be reconstructed functorially from the slice category Sch/S. We also show that every  auto-equivalence of the category of schemes is isomorphic to the identity. This removes all Noetherian and finite type hypotheses from  an earlier result of Mochizuki and completes a related result for rings due to Clark and Bergman (1973).