Applications of (higher) categorical trace I: the definition of AGCat
Dennis Gaitsgory, Nick Rozenblyum, Yakov Varshavsky
TL;DR
This paper introduces the formalism of algebro-geometric DG categories (AGCat), laying the groundwork for future applications in algebraic geometry and related fields.
Contribution
It formalizes the concept of AGCat based on Drinfeld's suggestion, providing a foundation for subsequent research and applications.
Findings
Formal definition of AGCat provided
Framework set for future applications in algebraic geometry
Lays groundwork for subsequent papers in the series
Abstract
In this paper we record the formalism of algebro-geometric DG categories (in short AGCat) following a suggestion of V. Drinfeld. This formalism will be applied to ``real-world" problems in papers sequel to this one, [GRV2] and [GRV3].
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Operator Algebra Research