Proper local complete intersection morphisms preserve perfect complexes

TL;DR

This paper proves that proper local complete intersection morphisms preserve perfect complexes without assuming projectivity or noetherian conditions, offering a new proof using derived algebraic geometry techniques.

Contribution

It provides a novel proof that proper local complete intersection morphisms preserve perfect complexes, extending previous results without restrictive assumptions.

Findings

Proper LCI morphisms preserve perfect complexes.

The proof avoids projectivity and noetherian assumptions.

Uses derived algebraic geometry techniques.

Abstract

Let $f : X \longrightarrow Y$ be a proper and local complete intersection morphism of schemes. We prove that $\mathbb{R}f_{*}$ 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.