Modular characteristic classes for representations over finite fields

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Modular characteristic classes for representations over finite fields. / Lahtinen, Anssi; Sprehn, David.

I: Advances in Mathematics, Bind 323, 2018, s. 1-37.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Lahtinen, A & Sprehn, D 2018, 'Modular characteristic classes for representations over finite fields', Advances in Mathematics, bind 323, s. 1-37. https://doi.org/10.1016/j.aim.2017.10.029

APA

Lahtinen, A., & Sprehn, D. (2018). Modular characteristic classes for representations over finite fields. Advances in Mathematics, 323, 1-37. https://doi.org/10.1016/j.aim.2017.10.029

Vancouver

Lahtinen A, Sprehn D. Modular characteristic classes for representations over finite fields. Advances in Mathematics. 2018;323:1-37. https://doi.org/10.1016/j.aim.2017.10.029

Author

Lahtinen, Anssi ; Sprehn, David. / Modular characteristic classes for representations over finite fields. I: Advances in Mathematics. 2018 ; Bind 323. s. 1-37.

Bibtex

@article{831c3a7d658c4f878013e5efbfaa9664,
title = "Modular characteristic classes for representations over finite fields",
abstract = "The cohomology of the degree-n general linear group over a finite field of characteristic p, with coefficients also in characteristic p, remains poorly understood. For example, the lowest degree previously known to contain nontrivial elements is exponential in n. In this paper, we introduce a new system of characteristic classes for representations over finite fields, and use it to construct a wealth of explicit nontrivial elements in these cohomology groups. In particular we obtain nontrivial elements in degrees linear in n. We also construct nontrivial elements in the mod p homology and cohomology of the automorphism groups of free groups, and the general linear groups over the integers. These elements reside in the unstable range where the homology and cohomology remain mysterious.",
keywords = "Automorphism groups of free groups, Characteristic classes, General linear groups, Group cohomology, Modular representations",
author = "Anssi Lahtinen and David Sprehn",
year = "2018",
doi = "10.1016/j.aim.2017.10.029",
language = "English",
volume = "323",
pages = "1--37",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Modular characteristic classes for representations over finite fields

AU - Lahtinen, Anssi

AU - Sprehn, David

PY - 2018

Y1 - 2018

N2 - The cohomology of the degree-n general linear group over a finite field of characteristic p, with coefficients also in characteristic p, remains poorly understood. For example, the lowest degree previously known to contain nontrivial elements is exponential in n. In this paper, we introduce a new system of characteristic classes for representations over finite fields, and use it to construct a wealth of explicit nontrivial elements in these cohomology groups. In particular we obtain nontrivial elements in degrees linear in n. We also construct nontrivial elements in the mod p homology and cohomology of the automorphism groups of free groups, and the general linear groups over the integers. These elements reside in the unstable range where the homology and cohomology remain mysterious.

AB - The cohomology of the degree-n general linear group over a finite field of characteristic p, with coefficients also in characteristic p, remains poorly understood. For example, the lowest degree previously known to contain nontrivial elements is exponential in n. In this paper, we introduce a new system of characteristic classes for representations over finite fields, and use it to construct a wealth of explicit nontrivial elements in these cohomology groups. In particular we obtain nontrivial elements in degrees linear in n. We also construct nontrivial elements in the mod p homology and cohomology of the automorphism groups of free groups, and the general linear groups over the integers. These elements reside in the unstable range where the homology and cohomology remain mysterious.

KW - Automorphism groups of free groups

KW - Characteristic classes

KW - General linear groups

KW - Group cohomology

KW - Modular representations

UR - http://www.scopus.com/inward/record.url?scp=85033568767&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2017.10.029

DO - 10.1016/j.aim.2017.10.029

M3 - Journal article

AN - SCOPUS:85033568767

VL - 323

SP - 1

EP - 37

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

ID: 215132889