Derived completion for comodules

Tobias Barthel; Drew Heard; Gabriel Valenzuela

doi:10.1007/s00229-018-1094-0

Derived completion for comodules

Tobias Barthel, Drew Heard, Gabriel Valenzuela^*

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

2 Citationer (Scopus)

14 Downloads (Pure)

Abstract

The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to comodule-theoretic completion, construct various local homology spectral sequences, and derive a tilting-theoretic interpretation of local duality for modules. Our results translate to quasi-coherent sheaves over global quotient stacks and feed into a novel approach to the chromatic splitting conjecture.

Originalsprog	Engelsk
Tidsskrift	Manuscripta Mathematica
Antal sider	30
ISSN	0025-2611
DOI	https://doi.org/10.1007/s00229-018-1094-0
Status	Udgivet - 1 mar. 2020

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10.1007/s00229-018-1094-0

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AU - Valenzuela, Gabriel

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AB - The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to comodule-theoretic completion, construct various local homology spectral sequences, and derive a tilting-theoretic interpretation of local duality for modules. Our results translate to quasi-coherent sheaves over global quotient stacks and feed into a novel approach to the chromatic splitting conjecture.

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Derived completion for comodules

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