The relative singularity category of a non-commutative resolution of singularities

Igor Burban; Martin Kalck

doi:10.1016/j.aim.2012.05.012

The relative singularity category of a non-commutative resolution of singularities

Igor Burban^*, Martin Kalck

^*Corresponding author for this work

School of Mathematics

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

Abstract / Description of output

In this article, we study a triangulated category associated with a non-commutative resolution of singularities. In particular, we give a complete description of this category in the case of a curve with nodal singularities, classifying its indecomposable objects and computing its Auslander-Reiten quiver and K-group. (C) 2012 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	414-435
Number of pages	22
Journal	Advances in Mathematics
Volume	231
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2012.05.012
Publication status	Published - 10 Sept 2012

Keywords / Materials (for Non-textual outputs)

Triangulated category
Non-commutative resolution
K-theory
Auslander-Reiten quiver
TRIANGULATED CATEGORIES
ALGEBRAS
GORENSTEIN

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10.1016/j.aim.2012.05.012

Cite this

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title = "The relative singularity category of a non-commutative resolution of singularities",

abstract = "In this article, we study a triangulated category associated with a non-commutative resolution of singularities. In particular, we give a complete description of this category in the case of a curve with nodal singularities, classifying its indecomposable objects and computing its Auslander-Reiten quiver and K-group. (C) 2012 Elsevier Inc. All rights reserved.",

keywords = "Triangulated category, Non-commutative resolution, K-theory, Auslander-Reiten quiver, TRIANGULATED CATEGORIES, ALGEBRAS, GORENSTEIN",

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AU - Burban, Igor

AU - Kalck, Martin

PY - 2012/9/10

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AB - In this article, we study a triangulated category associated with a non-commutative resolution of singularities. In particular, we give a complete description of this category in the case of a curve with nodal singularities, classifying its indecomposable objects and computing its Auslander-Reiten quiver and K-group. (C) 2012 Elsevier Inc. All rights reserved.

KW - Triangulated category

KW - Non-commutative resolution

KW - K-theory

KW - Auslander-Reiten quiver

KW - TRIANGULATED CATEGORIES

KW - ALGEBRAS

KW - GORENSTEIN

U2 - 10.1016/j.aim.2012.05.012

DO - 10.1016/j.aim.2012.05.012

M3 - Article

SN - 0001-8708

VL - 231

SP - 414

EP - 435

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

The relative singularity category of a non-commutative resolution of singularities

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

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