Derived completion for comodules

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Tobias Barthel, Drew Heard, Gabriel Valenzuela

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.

Original languageEnglish
JournalManuscripta Mathematica
Number of pages30
Publication statusE-pub ahead of print - 1 Jan 2019

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