Derived completion for comodules
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Derived completion for comodules. / Barthel, Tobias; Heard, Drew; Valenzuela, Gabriel.
I: Manuscripta Mathematica, Bind 161, 2020, s. 409–438.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Derived completion for comodules
AU - Barthel, Tobias
AU - Heard, Drew
AU - Valenzuela, Gabriel
PY - 2020
Y1 - 2020
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
VL - 161
SP - 409
EP - 438
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
SN - 0025-2611
ER -
ID: 212680679