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Journal Article

Derived completion for comodules

MPS-Authors
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Valenzuela,  Gabriel
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s00229-018-1094-0
(Publisher version)

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Fulltext (public)

1808.00895.pdf
(Preprint), 388KB

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Citation

Barthel, T., Heard, D., & Valenzuela, G. (2020). Derived completion for comodules. Manuscripta Mathematica, 161(3-4), 409-438. doi:10.1007/s00229-018-1094-0.


Cite as: https://hdl.handle.net/21.11116/0000-0006-0246-9
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.