Periodic free resolutions from twisted matrix factorizations

JOURNAL OF ALGEBRA

卷:455

Article

Cassidy, Thomas¹  Conner, Andrew²  Kirkman, Ellen³  Moore, W. Frank³ 

[1] Bucknell Univ, Dept Math, Lewisburg, PA 17837 USA

[2] St Marys Coll, Dept Math, Moraga, CA 94575 USA

[3] Wake Forest Univ, Dept Math, Winston Salem, NC 27109 USA

关键词: Matrix factorization;    Zhang twist;    Singularity category;    Minimal free resolution;    Maximal Cohen-Macaulay;   

DOI  :  10.1016/j.jalgebra.2016.01.037

来源: Elsevier

【 摘 要 】

The notion of a matrix factorization was introduced by Eisen bud in the commutative case in his study of bounded (periodic) free resolutions over complete intersections. Since then, matrix factorizations have appeared in a number of applications. In this work, we extend the notion of (homogeneous) matrix factorizations to regular normal elements of connected graded algebras over a field. Next, we relate the category of twisted matrix factorizations to an element over a ring and certain Zhang twists. We also show that in the setting of a quotient of a ring of finite global dimension by a normal regular element, every sufficiently high syzygy module is the cokernel of some twisted matrix factorization. Furthermore, we show that in the noetherian AS regular setting, there is an equivalence of categories between the homotopy category of twisted matrix factorizations and the singularity category of the hypersurface, following work of Orlov. (C) 2016 Published by Elsevier Inc.

【 授权许可】

Free