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arXiv · 1808.01695

Koszul algebras and quadratic duals in Galois cohomology

Jan Minac·Federico W. Pasini·Claudio Quadrelli·Nguyen Duy Tan
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Abstract

We investigate the Galois cohomology of finitely generated maximal pro-$p$ quotients of absolute Galois groups. Assuming the well-known conjectural description of these groups, we show that Galois cohomology has the PBW property. Hence in particular it is a Koszul algebra. This answers positively a conjecture by Positselski in this case. We also provide an analogous unconditional result about Pythagorean fields. Moreover, we establish some results that relate the quadratic dual of Galois cohomology with $p$-Zassenhaus filtration on the group. This paper also contains a survey of Koszul property in Galois cohomology and its relation with absolute Galois groups.

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Jan Minac, Federico W. Pasini, Claudio Quadrelli, Nguyen Duy Tan. 2020-12-31. Koszul algebras and quadratic duals in Galois cohomology. https://doi.org/10.1016/j.aim.2021.107569

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