For a prime number p, we give a new restriction on pro-p groups G which are realizable as the maximal pro-p Galois group GF(p) for a field F containing a root of unity of order p. This restriction arises from Kummer Theory and the structure of the maximal p-radical extension of F. We study it in the abstract context of pro-p groups G with a continuous homomorphism θ:G→1+pZp, and characterize it cohomologically, and in terms of 1-cocycles on G. This is used to produce new examples of pro-p groups which do not occur as maximal pro-p Galois groups of fields as above

The kummerian property and maximal pro-p galois groups

Quadrelli C.
2019-01-01

Abstract

For a prime number p, we give a new restriction on pro-p groups G which are realizable as the maximal pro-p Galois group GF(p) for a field F containing a root of unity of order p. This restriction arises from Kummer Theory and the structure of the maximal p-radical extension of F. We study it in the abstract context of pro-p groups G with a continuous homomorphism θ:G→1+pZp, and characterize it cohomologically, and in terms of 1-cocycles on G. This is used to produce new examples of pro-p groups which do not occur as maximal pro-p Galois groups of fields as above
2019
Maximal pro-p Galois groups; Galois cohomology; absolute Galois groups; oriented pro-p groups
Efrat, I.; Quadrelli, C.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2129370
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