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arxiv: 1210.2827 · v2 · pith:XFSSIRNAnew · submitted 2012-10-10 · 🧮 math.AG · math.KT

Proper local complete intersection morphisms preserve perfect complexes

B. To\"en This is my paper
classification 🧮 math.AG math.KT
keywords completecomplexesintersectionlocalnoetherianperfectproperalgebraic
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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.

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