The Brown-Peterson cohomology of the classifying spaces of the projective unitary groups 𝑃𝑈(𝑝) and exceptional Lie groups

Kameko, Masaki; Yagita, Nobuaki

doi:10.1090/s0002-9947-07-04425-x

Cited by 18 publications

(14 citation statements)

References 12 publications

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“…In [35], Vistoli determined the ring structures of A * P GLp and H * P GLp where p is an odd prime. In [20] (Kameko and Yagita), the additive structure of A * P GLp is obtained independently, as a corollary of the main results. Classes in the rings A * P GLn (resp.…”

Section: Introductionmentioning

confidence: 91%

Some torsion classes in the Chow ring and cohomology of $BPGL_n$

2019

Preprint

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In the integral cohomology ring of the classifying space of the projective linear group P GLn (over C), we find a collection of p-torsions y p,k of degree 2(p k+1 + 1) for any odd prime divisor p of n, and k ≥ 0.If in addition, p 2 ∤ n, there are p-torsion classes ρ p,k of degree p k+1 + 1 in the Chow ring of the classifying stack of P GLn, such that the cycle class map takes ρ p,k to y p,k .We present an application of the above classes regarding Chern subrings.

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Section: Introductionmentioning

confidence: 91%

Some torsion classes in the Chow ring and cohomology of $BPGL_n$

2019

Preprint

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“…This statement can be extracted from either [19] or [28] for BPU p when p is an odd prime. The special case of BPU 2 follows from [11] and the exceptional isomorphism PU 2 ∼ = SO 3 .…”

Section: The Low-degree Cohomology Of Bpu Nmentioning

confidence: 99%

The topological period-index problem over 6-complexes

Antieau

Williams

2013

Journal of Topology

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By comparing the Postnikov towers of the classifying spaces of projective unitary groups and the differentials in a twisted Atiyah-Hirzebruch spectral sequence, we deduce a lower bound on the topological index in terms of the period, and solve the topological version of the period-index problem in full for finite CW complexes of dimension less than 6. Conditions are established that, if they were met in the cohomology of a smooth complex 3-fold variety, would disprove the ordinary period-index conjecture. Examples of higher-dimensional varieties meeting these conditions are provided. We use our results to furnish an obstruction to realizing a period-2 Brauer class as the class associated to a sheaf of Clifford algebras, and varieties are constructed for which the total Clifford invariant map is not surjective. No such examples were previously known.

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“…In [45], Vistoli determined the graded abelian group structures of

A_{P G L_{p}}^{*}

and

H_{P G L_{p}}^{*}

for

p

an odd prime, and partially determined their ring structures. In Kameko and Yagita [25], the additive structure of

A_{P G L_{p}}^{*}

is obtained independently, as a corollary of the main results.…”

Section: Introductionmentioning

confidence: 96%

Some torsion classes in the Chow ring and cohomology of BPGLn

2020

J. London Math. Soc.

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In the integral cohomology ring of the classifying space of the projective linear group P GLn (over C), we find a collection of p-torsion classes y p,k of degree 2(p k+1 + 1) for any odd prime divisor p of n, and k ≥ 0. If, in addition, p 2 ∤ n, there are p-torsion classes ρ p,k of degree p k+1 + 1 in the Chow ring of the classifying stack of P GLn, such that the cycle class map takes ρ p,k to y p,k. We present an application of the above classes regarding Chern subrings.

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The Brown-Peterson cohomology of the classifying spaces of the projective unitary groups 𝑃𝑈(𝑝) and exceptional Lie groups

Abstract: For a fixed prime p, we compute the Brown-Peterson cohomologies of classifying spaces of P U(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that BP * (BP U(p)) and K(n) * (BP U(p)) are even dimensionally generated.

Cited by 18 publications

References 12 publications

Some torsion classes in the Chow ring and cohomology of $BPGL_n$

Some torsion classes in the Chow ring and cohomology of $BPGL_n$

The topological period-index problem over 6-complexes

Some torsion classes in the Chow ring and cohomology of BPGLn

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