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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
2106.03675.pdf
non disponibili
Descrizione: Preprint presente su arxiv
Tipologia:
Documento in Pre-print
Licenza:
Creative commons
Dimensione
335.72 kB
Formato
Adobe PDF
|
335.72 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
