Geodesic
Les classes de Chern modulo $p$ d'une représentation régulière.
Documenta mathematica, Tome 4 (1999), pp. 167-178.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $G$ be a finite group and $\rho$ a complex linear representation of $G$. In 1961, Atiyah and Venkov independently defined Chern classes $c_i(\rho)$ with values in the integral or mod $p$ cohomology of $G$. We consider here the mod $p$ Chern classes of the regular representation $r_G$ of $G$. Venkov claimed that $c_i(r_G)=0$ for $i^n-p^{n-1}$, where $p^n$ is the highest power of $p$ dividing $|G|$; however his proof is only valid for $G$ elementary abelian. In this note, we show Venkov's assertion is valid for any $G$. The proof also shows that the $c_i(r_G)$ are $p$-powers of cohomology classes invariant by $Aut(G)$ as soon as $G$ is a non-abelian $p$-group.
Classification : 20J06, 20C15
Keywords: finite groups, Chern classes, regular representation 
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     author = {Kahn, Bruno},
     title = {Les classes de {Chern} modulo $p$ d'une repr\'esentation r\'eguli\`ere.},
     journal = {Documenta mathematica},
     pages = {167--178},
     publisher = {mathdoc},
     volume = {4},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1999__4__a14/}
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Kahn, Bruno. Les classes de Chern modulo $p$ d'une représentation régulière.. Documenta mathematica, Tome 4 (1999), pp. 167-178. http://geodesic.mathdoc.fr/item/DOCMA_1999__4__a14/