On the Chow ring of the classifying stack of PGL3
Abstract
We compute generators for the Chow ring of the classifying space of PGL3 (over the complex numbers) as defined by Totaro. We also find enough relations after inverting 3. We show that this ring is not generated by Chern classes (this is the first example of this kind among classical groups) and prove that Totaro's refined cycle class map to a quotient of complex cobordism of BPGL3 is surjective
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