On the Chow ring of the classifying stack of PGL₃

1999/04/14 by Gabriele Vezzosi, Vezzosi, Gabriele
Mathematics · #14C15 #20G20 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT #msc:14C15 #msc:20G20

paper · pdf · doi:10.48550/arxiv.math/9904063

42 pages; TOC file (run LaTeX 3 times)

arxiv created 1999/04/14 · arxiv updated 2009/11/30

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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