On central extensions of a Galois extension of algebraic number fields

Procyclic Galois Extensions of Algebraic Number Fields

6 1 Iwasawa’s theory of Zp-extensions 9 1.

Galois Extensions of Hilbertian Fields

We prove the following result: Theorem. Let K be a countable Hilbertian field, S a finite set of local primes of K, and e ≥ 0 an integer. Then, for almost all ∈ G(K)e, the field Ks[ ] ∩Ktot,S is PSC. Here a local prime is an equivalent class p of absolute values of K whose completion is a local field, K̂p. Then Kp = Ks ∩ K̂p and Ktot,S = T p∈S T σ∈G(K) K σ p . G(K) stands for the absolute Galois ...

Algebraic Geometry of Hopf - Galois Extensions

We continue the investigation of Hopf-Galois extensions with central invariants started in [30]. Our objective is not to imitate algebraic geometry using Hopf-Galois extension but to understand their geometric properties. Let H be a finite-dimensional Hopf algebra over a ground field k. Our main object of study is an H-Galois extension U ⊇ O such that O is a central subalgebra of U . Let us bri...

Compositum of Galois Extensions of Hilbertian Fields

On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields

Let C be a smooth absolutely irreducible curve of genus g ≥ 1 defined over Fq, the finite field of q elements. Let #C(Fqn) be the number of Fqn -rational points on C. Under a certain multiplicative independence condition on the roots of the zetafunction of C, we derive an asymptotic formula for the number of n = 1, . . . , N such that (#C(Fqn) − q − 1)/2gq belongs to a given interval I ⊆ [−1, 1...