Gabriel’s theorem and birational geometry

Calabrese, John; Pirisi, Roberto

doi:10.1090/proc/14990

Gabriel’s theorem and birational geometry
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by John Calabrese and Roberto Pirisi PDF

Proc. Amer. Math. Soc. 149 (2021), 907-922 Request permission

Abstract:

Extending work of Meinhardt and Partsch, we prove that two varieties are isomorphic away from a subset of a given dimension if and only if certain quotients of their categories of coherent sheaves are equivalent. This result interpolates between Gabriel’s reconstruction theorem and the fact that two varieties are birational if and only if they have the same function field.

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