Let p be a prime, and Fp the field with p elements. We prove that if G is a mild pro-p group with quadratic Fp-cohomology algebra H∙(G,Fp), then the algebras H∙(G,Fp) and grFp[[G]] - the latter being induced by the quotients of consecutive terms of the p-Zassenhaus filtration of G - are both Koszul, and they are quadratically dual to each other. Consequently, if the maximal pro-p Galois group of a field is mild, then Positselski's and Weigel's Koszulity conjectures hold true for such a field.

Mild pro-p groups and the koszulity conjectures

Claudio Quadrelli;
2022-01-01

Abstract

Let p be a prime, and Fp the field with p elements. We prove that if G is a mild pro-p group with quadratic Fp-cohomology algebra H∙(G,Fp), then the algebras H∙(G,Fp) and grFp[[G]] - the latter being induced by the quotients of consecutive terms of the p-Zassenhaus filtration of G - are both Koszul, and they are quadratically dual to each other. Consequently, if the maximal pro-p Galois group of a field is mild, then Positselski's and Weigel's Koszulity conjectures hold true for such a field.
2022
2022
https://www.sciencedirect.com/science/article/abs/pii/S0723086922000196
Galois cohomology; Koszul algebras; Maximal pro-p Galois groups; Mild pro-p groups; Quadratic algebras;
Minac, Jan; Pasini, Federico; Quadrelli, Claudio; Duy Tan, Nguyen
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2131204
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