A note on homological dimension of a family of coherent sheaves
Nadezda V. Timofeeva
TL;DR
This paper presents a theorem linking the homological dimension of a family of coherent sheaves over a scheme to the homological dimension of its restriction to the scheme's reduction, simplifying analysis in algebraic geometry.
Contribution
It introduces a new theorem that relates the homological dimension of coherent sheaves on a scheme to that on its reduction, aiding in the study of their properties.
Findings
Established a method to determine homological dimension via restrictions
Simplified analysis of coherent sheaves on schemes
Provided theoretical foundation for future research
Abstract
We prove a theorem on how a conclusion on homological dimension of a family of coherent sheaves over a scheme can be done from homological dimension of the restriction of this family to the reduction of the base.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models