Derived completion for comodules
Algebraic Topology
2019-01-18 v2 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.
Cite
@article{arxiv.1808.00895,
title = {Derived completion for comodules},
author = {Tobias Barthel and Drew Heard and Gabriel Valenzuela},
journal= {arXiv preprint arXiv:1808.00895},
year = {2019}
}
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