Etale cohomology, purity and formality with torsion coefficients

Abstract

We use Galois group actions on étale cohomology to prove results of formality for dg-operads and dg-algebras with torsion coefficients. Our theory applies, among other related constructions, to the dg-operad of singular chains on the operad of little disks and to the dg-algebra of singular cochains on the configuration space of points in the complex space. The formality that we obtain is only up to a certain degree, which depends on the cardinality of the field of coefficients.

arXiv comment25 pages. This is a corrected version of the published version (see the note at the begining)

References in corpus (10)

• Combinatorial operad actions on cochains
• Cochains and Homotopy Type
• Pro-categories in homotopy theory
• Operads of genus zero curves and the Grothendieck-Teichmüller group
• Mixed Hodge structures and formality of symmetric monoidal functors
• Cohomology of generalized configuration spaces
• Non-commutative formality implies commutative and Lie formality
• Godement resolutions and sheaf homotopy theory
• On the formality of the little disks operad in positive characteristic
• Koszul A-infinity algebras and free loop space homology

Cited by in corpus (6)

• On the formality of the little disks operad in positive characteristic
• Moduli of framed formal curves
• Formality of little disks and algebraic geometry
• An operadic proof of the BTT Theorem
• E2 formality via obstruction theory
• Sinha's spectral sequence for long knots in codimension one and non-formality of the little 2-disks operad