## Annals of K-Theory

### On the cycle map of a finite group

Masaki Kameko

#### Abstract

Let $p$ be an odd prime number. We show that there exists a finite group of order $pp+3$ for which the mod $p$ cycle map from the mod $p$ Chow ring of its classifying space to its ordinary mod $p$ cohomology is not injective.

#### Article information

Source
Ann. K-Theory, Volume 2, Number 1 (2017), 47-72.

Dates
Revised: 9 January 2016
Accepted: 2 February 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.akt/1510841624

Digital Object Identifier
doi:10.2140/akt.2017.2.47

Mathematical Reviews number (MathSciNet)
MR3599516

Zentralblatt MATH identifier
1349.14019

#### Citation

Kameko, Masaki. On the cycle map of a finite group. Ann. K-Theory 2 (2017), no. 1, 47--72. doi:10.2140/akt.2017.2.47. https://projecteuclid.org/euclid.akt/1510841624

#### References

• B. Antieau and B. Williams, “The topological period-index problem over 6-complexes”, J. Topol. 7:3 (2014), 617–640.
• S. Araki, “Steenrod reduced powers in the spectral sequences associated with a fibering, II”, Mem. Fac. Sci. Kyusyu Univ. Ser. A. Math. 11 (1957), 81–97.
• P. F. Baum and W. Browder, “The cohomology of quotients of classical groups”, Topology 3 (1965), 305–336.
• M. Kameko, “On the integral Tate conjecture over finite fields”, Math. Proc. Cambridge Philos. Soc. 158:3 (2015), 531–546.
• M. Kameko and N. Yagita, “The Brown–Peterson cohomology of the classifying spaces of the projective unitary groups ${\rm PU}(p)$ and exceptional Lie groups”, Trans. Amer. Math. Soc. 360:5 (2008), 2265–2284.
• A. Kono, M. Mimura, and N. Shimada, “Cohomology of classifying spaces of certain associative $H$-spaces”, J. Math. Kyoto Univ. 15:3 (1975), 607–617.
• B. Totaro, “The Chow ring of a classifying space”, pp. 249–281 in Algebraic $K$-theory (Seattle, WA, 1997), edited by W. Raskind and C. Weibel, Proc. Sympos. Pure Math. 67, Amer. Math. Soc., Providence, RI, 1999.
• B. Totaro, Group cohomology and algebraic cycles, Cambridge Tracts in Mathematics 204, Cambridge University Press, 2014.
• A. Vistoli, “On the cohomology and the Chow ring of the classifying space of ${\rm PGL}\sb p$”, J. Reine Angew. Math. 610 (2007), 181–227.