Low Degree Cohomology of Frobenius Kernels

Ngo, Nham V.

doi:10.1007/978-3-030-11521-0_13

Nham V. Ngo⁶

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Abstract

Let G be a simple algebraic group defined over an algebraically closed field of characteristic \(p>0\). For a positive integer r, let \(G_r\) be the r-th Frobenius kernel of G. We determine in this paper a number m such that the cohomology \(\text {H}^n(G_r,k)\) is isomorphic to \(\text {H}^n(G_1,k)\) for all \(n\le m\) where m depends on p and the type of G.

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References

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Acknowledgements

This paper is a part of the author’s dissertation at the University of Georgia. He is grateful for the guidedance of his Ph.D. advisor Daniel K. Nakano and secondary advisor Christopher M. Drupieski.

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University of North Georgia–Gainesville, Oakwood, GA, 30566, USA
Nham V. Ngo

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Nham V. Ngo
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Correspondence to Nham V. Ngo .

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Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA
Jörg Feldvoss
Department of Mathematics, Spring Hill College, Mobile, AL, USA
Lauren Grimley
Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA
Drew Lewis
Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA
Andrei Pavelescu
Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA
Cornelius Pillen

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Ngo, N.V. (2019). Low Degree Cohomology of Frobenius Kernels. In: Feldvoss, J., Grimley, L., Lewis, D., Pavelescu, A., Pillen, C. (eds) Advances in Algebra. SRAC 2017. Springer Proceedings in Mathematics & Statistics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-030-11521-0_13

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DOI: https://doi.org/10.1007/978-3-030-11521-0_13
Published: 27 February 2019
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11520-3
Online ISBN: 978-3-030-11521-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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