Let p be a prime. We produce two new families of pro-p groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro-p groups. Moreover, we show in these families one has one-relator pro-p groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.
Two families of pro-p groups that are not Absolute Galois Groups
Quadrelli, C
2022-01-01
Abstract
Let p be a prime. We produce two new families of pro-p groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro-p groups. Moreover, we show in these families one has one-relator pro-p groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.