Koszul complexes and fully faithful integral functors
Fernando Sancho de Salas
TL;DR
This paper characterizes certain objects in the derived category using Koszul complexes and generalizes criteria for when an integral functor is fully faithful across arbitrary schemes.
Contribution
It introduces a new characterization of objects supported on closed subschemes and extends fully faithfulness criteria for integral functors to broader scheme classes.
Findings
Objects supported on closed subschemes are characterized via Koszul complexes
Fully faithfulness criteria are generalized to arbitrary schemes
Provides new tools for understanding derived categories and functor properties
Abstract
We characterise those objects in the derived category of a scheme which are a sheaf supported on a closed subscheme in terms of Koszul complexes. This is applied to generalize to arbitrary schemes the fully faithfullness criteria of an integral functor.
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