Work

The Serre-Grothendieck Finiteness Theorem for the cohomology of coherent sheaves

Year: 2026

Type: preprint

Abstract: We prove the converse of the Serre-Grothendieck finiteness theorem for the cohomology of coherent sheaves, originally due to Lipman. This result characterizes proper morphisms as those morphisms whose derived pushforward preserves pseudo-coherent complexes. Although the derived pushforward does not reflect pseudo-coherence, we prove that it does after twisting by all perfect complexes. This provides a new characterization of properness.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.28945

Author: Sanders, Beren

Institution: University of California, Santa Cruz

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: University of California, Santa Cruz

OpenAlex ID: W7214354830

Cites: 2

Cited by:

Related to: 10