Proper local complete intersection morphisms preserve perfect complexes

Abstract

Let $f:X⟶Y$ be a proper and local complete intersection morphism of schemes. We prove that $\mathbb{R}{f}_{\ast }$ preserves perfect complexes, without any projectivity or noetherian assumptions. This provides a different proof of a theorem by Neeman and Lipman based on techniques from derived algebraic geometry to proceed a reduction to the noetherian case.

13 pages. Second version: the author was not aware of previous references and the fact that the main result was already known. The text has been corrected accordingly, but the mathematical part remains unchanged

References in corpus (1)

• Higher and derived stacks: a global overview