Derived completion for comodules

TY - JOUR

T1 - Derived completion for comodules

AU - Barthel, Tobias

AU - Heard, Drew

AU - Valenzuela, Gabriel

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85059507253&partnerID=8YFLogxK

U2 - 10.1007/s00229-018-1094-0

DO - 10.1007/s00229-018-1094-0

M3 - Journal article

AN - SCOPUS:85059507253

SN - 0025-2611

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

ER -