Galois structures on plane compacts

Galois structures

Counting Hopf Galois Structures on Non-abelian Galois Field Extensions

Let L be a field which is a Galois extension of the field K with Galois group G. Greither and Pareigis [GP87] showed that for many G there exist K-Hopf algebras H other than the group ring KG which make L into an H-Hopf Galois extension of K (or a Galois H∗object in the sense of Chase and Sweedler [CS69]). Using Galois descent they translated the problem of determining the Hopf Galois structure...

On the Galois correspondence for Hopf Galois structures

We study the question of the surjectivity of the Galois correspondence from subHopf algebras to subfields given by the Fundamental Theorem of Galois Theory for abelian Hopf Galois structures on a Galois extension of fields with Galois group Γ, a finite abelian p-group. Applying the connection between regular subgroups of the holomorph of a finite abelian p-group (G,+) and associative, commutati...

On Hopf Galois structures and complete groups

Let L be a Galois extension of K, fields, with Galois group Γ. We obtain two results. First, if Γ = Hol(Zpe ), we determine the number of Hopf Galois structures on L/K where the associated group of the Hopf algebra H is Γ (i.e. L⊗K H ∼= L[Γ]). Now let p be a safeprime, that is, p is a prime such that q = (p−1)/2 > 2 is also prime. If L/K is Galois with group Γ = Hol(Zp), p a safeprime, then for...

Projective Group Structures as Absolute Galois Structures

We prove: A proper profinite group structure G is projective if and only if G is the absolute Galois group structure of a proper field-valuation structure with block approximation. MR Classification: 12E30 Directory: \Jarden\Diary\HJPa 30 April, 2008 * Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation. ** Research partially don...