
TL;DR
This paper constructs a finite group of order p^{p+3} demonstrating that the mod p cycle map from the Chow ring to cohomology can fail to be injective, revealing new complexities in algebraic topology.
Contribution
It provides the first known example of a finite group where the mod p cycle map is not injective, highlighting limitations of existing cohomological tools.
Findings
Existence of a finite group with non-injective cycle map
The order of the constructed group is p^{p+3}
Shows limitations of the cycle map in algebraic topology
Abstract
Let p be an odd prime number. We show that there exists a finite group of order p^{p+3} whose the mod p cycle map from the mod p Chow ring of its classifying space to its ordinary mod p cohomology is not injective.
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