Tobias Barthel, Drew Heard, Gabriel Valenzuela
Published 2018-08-01Version 1
The objective of this paper is to study completions and the 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: All comments are welcome. arXiv admin note: text overlap with arXiv:1511.03526
The Chromatic Splitting Conjecture at n=p=2
The rational homotopy of the K(2)-local sphere and the chromatic splitting conjecture for the prime 3 and level 2
A short introduction to the telescope and chromatic splitting conjectures
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