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
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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