Difference sheaves and torsors
Marcin Cha{\l}upnik, Piotr Kowalski
TL;DR
This paper develops a sheaf theory framework within difference algebraic geometry, introducing new categories and cohomology theories that extend classical concepts to the difference setting.
Contribution
It introduces difference sheaves, cohomology, and torsors, extending classical algebraic geometry tools to the difference algebra context.
Findings
Established difference Galois cohomology
Defined difference Picard group
Developed theory of difference torsors
Abstract
We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference Picard group and a good theory of difference torsors.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra