TL;DR
This paper introduces prestacks of Tate type, develops Tate-coherent sheaves, and defines a dualizing gerbe, advancing the geometric framework for Tate schemes in algebraic geometry.
Contribution
It formalizes the concept of prestacks of Tate type and develops a Tate-coherent sheaf theory, providing new tools for studying Tate schemes.
Findings
Defined prestacks of Tate type with geometric conditions
Developed Tate-coherent sheaves formalism
Introduced dualizing gerbe for Tate schemes
Abstract
This paper introduces the notion of prestacks of Tate type and studies natural geometric conditions on them. We also develop a formalism of Tate-coherent sheaves and define a dualizing gerbe for Tate schemes locally almost of finite type.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory