## Modular characteristic classes for representations over finite fields

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#### Standard

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 tidsskriftTidsskriftartikelForskningfagfællebedømt

#### 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",
issn = "0001-8708",

}

#### 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