On the integral Tate conjecture over finite fields

Kameko, Masaki

doi:10.1017/s0305004115000134

Cited by 13 publications

(13 citation statements)

References 10 publications

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“…In the special case r = 1, much of the constructions presented in this section appears in various works such as [43], [25], and [29].…”

Section: A Non-toral P-elementary Subgroup Of P U P Rmentioning

confidence: 99%

A distinguished subring of the Chow ring and cohomology of $BPGL_n$

Gu¹

2020

Preprint

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We determine a subring of the Chow ring and the cohomology of BP GLn, the classifying space of the projective linear group of degree n over complex numbers, and explain a way in which this computation might play a role in the period-index problem. In addition, we show that the Chow ring of BP GLn is not generated by the Chern classes of linear representations of P GLn. Contents 1. Introduction 1 2. Preliminaries on motivic homotopy theory 5 3. The classes ρ p,k and y p,k 15 4. On the cohomology of the extraspecial p-groups p 1+2r + 17 5. A non-toral p-elementary subgroup of P U p r 20 6. A polynomial relation 26 7. The period-index problem 31 8. On the Chern subring of CH * (BP GL n ) (p) 33 Appendix A. A partial Jacobian criterion over perfect fields of positive characteristics 33 References 34Notations.

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“…In the special case r = 1, much of the constructions presented in this section appears in various works such as [43], [25], and [29].…”

Section: A Non-toral P-elementary Subgroup Of P U P Rmentioning

confidence: 99%

A distinguished subring of the Chow ring and cohomology of $BPGL_n$

Gu¹

2020

Preprint

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“…We proved (f • g) * (ρ(x 4 )) = Q 0 (x 1 y 1 z 1 ) in [5]. Because we use a similar but slightly different argument in the proof of Theorem 1.2 for K = H, we prove the following weaker form in this paper.…”

Section: The Mod P Cycle Map For Gmentioning

confidence: 92%

On the cycle map of a finite group

Kameko

2017

AKT

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“…In [7], counterexamples for the integral Hodge and Tate conjectures modulo torsion through the topological approach were given by Pirutka and Yagita using exceptional groups G 2 , F 4 , E 8 which contain elementary abelian p-subgroups (Z/ p) 3 for p = 2, 3, 5, respectively. In [4], the author replaced the exceptional groups by G 1 = (SL p × SL p )/μ p for all prime numbers p, where SL p is the special linear group over the complex numbers and μ p is the center of SL p and μ p acts on SL p × SL p diagonally.…”

Section: Introductionmentioning

confidence: 99%