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  Derived completion for comodules

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0006-0246-9 Version Permalink: https://hdl.handle.net/21.11116/0000-0006-0247-8
Genre: Journal Article

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This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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 Creators:
Barthel, Tobias, Author
Heard, Drew, Author
Valenzuela, Gabriel1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Topology,Mathematics, Commutative Algebra
 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: Final version to appear in manuscripta mathematica. A preliminary version of the results in the first two sections of this article was previously contained in the joint work of the authors at arXiv:1511.03526
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 Rev. Type: Peer
 Identifiers: arXiv: 1808.00895
DOI: 10.1007/s00229-018-1094-0
URI: http://arxiv.org/abs/1808.00895
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Title: Manuscripta Mathematica
  Abbreviation : manuscripta math.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 161 (3-4) Sequence Number: - Start / End Page: 409 - 438 Identifier: -