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Mathematics > Algebraic Topology

arXiv:1808.00895 (math)
[Submitted on 1 Aug 2018 (v1), last revised 17 Jan 2019 (this version, v2)]

Title:Derived completion for comodules

Authors:Tobias Barthel, Drew Heard, Gabriel Valenzuela
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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.
Comments: 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
Subjects: Algebraic Topology (math.AT); Commutative Algebra (math.AC)
MSC classes: 55P60 (13D45, 14B15, 55U35)
Report number: CPH-SYM-DNRF92
Cite as: arXiv:1808.00895 [math.AT]
  (or arXiv:1808.00895v2 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.1808.00895
Related DOI: https://doi.org/10.1007/s00229-018-1094-0

Submission history

From: Gabriel Valenzuela [view email]
[v1] Wed, 1 Aug 2018 09:01:11 UTC (33 KB)
[v2] Thu, 17 Jan 2019 13:00:18 UTC (34 KB)
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