Free (Z/p)n-complexes and p-DG modules

Jeremiah Heller; Marc Stephan

doi:10.1016/j.jalgebra.2020.07.028

Free (Z/p)ⁿ-complexes and p-DG modules

Jeremiah Heller, Marc Stephan

Mathematics

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

Abstract

We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring F_p[G] of an elementary abelian p-group G in terms of commutative algebra. This extends results of Carlsson for p=2 to all primes. As an intermediate step, we construct an embedding of the derived category of perfect chain complexes over F_p[G] into the derived category of p-DG modules over a polynomial ring.

Original language	English (US)
Pages (from-to)	221-254
Number of pages	34
Journal	Journal of Algebra
Volume	565
DOIs	https://doi.org/10.1016/j.jalgebra.2020.07.028
State	Published - Jan 1 2021

Keywords

Free (Z/p)-action
Perfect complex
Toral rank
p-DG module

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1016/j.jalgebra.2020.07.028

Library availability

Discover UIUC Full Text

Cite this

@article{13fc6749b7f94d0eb17dc58b403cfe80,

title = "Free (Z/p)n-complexes and p-DG modules",

abstract = "We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring Fp[G] of an elementary abelian p-group G in terms of commutative algebra. This extends results of Carlsson for p=2 to all primes. As an intermediate step, we construct an embedding of the derived category of perfect chain complexes over Fp[G] into the derived category of p-DG modules over a polynomial ring.",

keywords = "Free (Z/p)-action, Perfect complex, Toral rank, p-DG module",

author = "Jeremiah Heller and Marc Stephan",

note = "Funding Information: Jeremiah Heller was supported by NSF Grant DMS-1710966 . Marc Stephan was supported by SNSF grant 158932 . Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

month = jan,

day = "1",

doi = "10.1016/j.jalgebra.2020.07.028",

language = "English (US)",

volume = "565",

pages = "221--254",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Free (Z/p)n-complexes and p-DG modules

AU - Heller, Jeremiah

AU - Stephan, Marc

PY - 2021/1/1

Y1 - 2021/1/1

N2 - We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring Fp[G] of an elementary abelian p-group G in terms of commutative algebra. This extends results of Carlsson for p=2 to all primes. As an intermediate step, we construct an embedding of the derived category of perfect chain complexes over Fp[G] into the derived category of p-DG modules over a polynomial ring.

AB - We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring Fp[G] of an elementary abelian p-group G in terms of commutative algebra. This extends results of Carlsson for p=2 to all primes. As an intermediate step, we construct an embedding of the derived category of perfect chain complexes over Fp[G] into the derived category of p-DG modules over a polynomial ring.

KW - Free (Z/p)-action

KW - Perfect complex

KW - Toral rank

KW - p-DG module

UR - http://www.scopus.com/inward/record.url?scp=85090736240&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85090736240&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2020.07.028

DO - 10.1016/j.jalgebra.2020.07.028

M3 - Article

AN - SCOPUS:85090736240

SN - 0021-8693

VL - 565

SP - 221

EP - 254

JO - Journal of Algebra

JF - Journal of Algebra

ER -