Cohomology of Profinite Groups

Harari, David

doi:10.1007/978-3-030-43901-9_4

David Harari¹¹

Part of the book series: Universitext ((UTX))

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Abstract

This chapter extends all results of Chap. 1 to profinite groups.

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Notes

1.
Thanks to Miaofen Chen for pointing out this difficulty, and to J. Riou for suggesting the simple method relying on Lemma 4.7 to deal with it. My initial argument was more complicated.
2.
There is a small subtlety here: to imitate the proof for G finite, we must either use Proposition 4.25, or the slightly weaker fact that an induced \(G\)-module \(I_G(A)\) is acyclic for \(H^0(H,.)\), which is the object of Exercise 4.4.

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Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay, Orsay, France
David Harari

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Harari, D. (2020). Cohomology of Profinite Groups. In: Galois Cohomology and Class Field Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-43901-9_4

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DOI: https://doi.org/10.1007/978-3-030-43901-9_4
Published: 24 June 2020
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43900-2
Online ISBN: 978-3-030-43901-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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