Milnor descent for cohesive dg-categories

Oren Ben-Bassat; Jonathan Block

doi:10.1017/is013007003jkt236

Milnor descent for cohesive dg-categories

Oren Ben-Bassat
, Jonathan Block

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the functor from curved differential graded algebras to differential graded categories, defined by the second author, sends Cartesian diagrams to homotopy Cartesian diagrams, under certain reasonable hypotheses. This is an extension to the arena of dg-categories of a construction of projective modules due to Milnor. As an example, we show that the functor satisfies descent for certain partitions of a complex manifold.

Original language	English
Pages (from-to)	433-459
Number of pages	27
Journal	Journal of K-Theory
Volume	12
Issue number	3
DOIs	https://doi.org/10.1017/is013007003jkt236
State	Published - 2013
Externally published	Yes

Keywords

Mayer-Vietoris
descent
dg categories
projective modules

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1017/is013007003jkt236

Cite this

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title = "Milnor descent for cohesive dg-categories",

abstract = "We show that the functor from curved differential graded algebras to differential graded categories, defined by the second author, sends Cartesian diagrams to homotopy Cartesian diagrams, under certain reasonable hypotheses. This is an extension to the arena of dg-categories of a construction of projective modules due to Milnor. As an example, we show that the functor satisfies descent for certain partitions of a complex manifold.",

keywords = "Mayer-Vietoris, descent, dg categories, projective modules",

author = "Oren Ben-Bassat and Jonathan Block",

note = "Funding Information: The first author acknowledges the support of the European Commission under the Marie Curie Programme for the IEF grant which enabled this research to take place. The contents of this article reflect the views of the two authors and not the views of the European Commission. Funding Information: J.B. partially supported by NSF grant DMS10-07113.",

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language = "English",

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T1 - Milnor descent for cohesive dg-categories

AU - Ben-Bassat, Oren

AU - Block, Jonathan

N1 - Funding Information: The first author acknowledges the support of the European Commission under the Marie Curie Programme for the IEF grant which enabled this research to take place. The contents of this article reflect the views of the two authors and not the views of the European Commission. Funding Information: J.B. partially supported by NSF grant DMS10-07113.

PY - 2013

Y1 - 2013

N2 - We show that the functor from curved differential graded algebras to differential graded categories, defined by the second author, sends Cartesian diagrams to homotopy Cartesian diagrams, under certain reasonable hypotheses. This is an extension to the arena of dg-categories of a construction of projective modules due to Milnor. As an example, we show that the functor satisfies descent for certain partitions of a complex manifold.

AB - We show that the functor from curved differential graded algebras to differential graded categories, defined by the second author, sends Cartesian diagrams to homotopy Cartesian diagrams, under certain reasonable hypotheses. This is an extension to the arena of dg-categories of a construction of projective modules due to Milnor. As an example, we show that the functor satisfies descent for certain partitions of a complex manifold.

KW - Mayer-Vietoris

KW - descent

KW - dg categories

KW - projective modules

UR - https://www.scopus.com/pages/publications/84897853231

U2 - 10.1017/is013007003jkt236

DO - 10.1017/is013007003jkt236

M3 - Article

SN - 1865-2433

VL - 12

SP - 433

EP - 459

JO - Journal of K-Theory

JF - Journal of K-Theory

IS - 3

ER -

Milnor descent for cohesive dg-categories

Abstract

Keywords

ASJC Scopus subject areas

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