Tensor product of dualizing complexes over a field

Liran Shaul

doi:10.1216/JCA-2018-10-2-243

Tensor product of dualizing complexes over a field

Liran Shaul

Department of Mathematics

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

2 Scopus citations

Abstract

Let k[fraktur] be a field, and let X and Y be two locally noetherian k[fraktur]-schemes (respectively, k[fraktur]-formal schemes) with dualizing complexes R_X and R_Y, respectively. We show that R_X [squared times]k[fraktur] R_Y (respectively, its derived completion) is a dualizing complex over X ×k[fraktur] Y if and only if X ×k[fraktur] Y is locally noetherian of finite Krull dimension.

Original language	English
Pages (from-to)	243-263
Number of pages	21
Journal	Journal of Commutative Algebra
Volume	10
Issue number	2
DOIs	https://doi.org/10.1216/JCA-2018-10-2-243
State	Published - 1 Jan 2018

Keywords

Adic completion
Dualizing complex

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1216/JCA-2018-10-2-243

Cite this

@article{805aac6bc8104867ac3b28616cf8564e,

title = "Tensor product of dualizing complexes over a field",

abstract = "Let k[fraktur] be a field, and let X and Y be two locally noetherian k[fraktur]-schemes (respectively, k[fraktur]-formal schemes) with dualizing complexes RX and RY, respectively. We show that RX [squared times]k[fraktur] RY (respectively, its derived completion) is a dualizing complex over X ×k[fraktur] Y if and only if X ×k[fraktur] Y is locally noetherian of finite Krull dimension.",

keywords = "Adic completion, Dualizing complex",

author = "Liran Shaul",

note = "Publisher Copyright: {\textcopyright} 2018 Rocky Mountain Mathematics Consortium.",

year = "2018",

month = jan,

day = "1",

doi = "10.1216/JCA-2018-10-2-243",

language = "English",

volume = "10",

pages = "243--263",

journal = "Journal of Commutative Algebra",

issn = "1939-0807",

publisher = "Rocky Mountain Mathematics Consortium",

number = "2",

}

TY - JOUR

T1 - Tensor product of dualizing complexes over a field

AU - Shaul, Liran

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let k[fraktur] be a field, and let X and Y be two locally noetherian k[fraktur]-schemes (respectively, k[fraktur]-formal schemes) with dualizing complexes RX and RY, respectively. We show that RX [squared times]k[fraktur] RY (respectively, its derived completion) is a dualizing complex over X ×k[fraktur] Y if and only if X ×k[fraktur] Y is locally noetherian of finite Krull dimension.

AB - Let k[fraktur] be a field, and let X and Y be two locally noetherian k[fraktur]-schemes (respectively, k[fraktur]-formal schemes) with dualizing complexes RX and RY, respectively. We show that RX [squared times]k[fraktur] RY (respectively, its derived completion) is a dualizing complex over X ×k[fraktur] Y if and only if X ×k[fraktur] Y is locally noetherian of finite Krull dimension.

KW - Adic completion

KW - Dualizing complex

UR - http://www.scopus.com/inward/record.url?scp=85051596456&partnerID=8YFLogxK

U2 - 10.1216/JCA-2018-10-2-243

DO - 10.1216/JCA-2018-10-2-243

M3 - Article

AN - SCOPUS:85051596456

SN - 1939-0807

VL - 10

SP - 243

EP - 263

JO - Journal of Commutative Algebra

JF - Journal of Commutative Algebra

IS - 2

ER -

Tensor product of dualizing complexes over a field

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this