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Finally using class field theory and [2], we determine the ramification groups of G p ( K ) (we distinguish the case when K is unramified from the case when K is totally ramified,
The deepest input will be Lemma 2.1 be- low which only requires pre-Prime Number Theorem elementary methods for its proof (in Tenenbaum’s [11] introductory book on analytic
5.1. Preliminaries on twisted forms. We saw in the previous section that every quadric surface V q is an element of T.. Let X/k be a quadric surface.. The proof of Theorem 7b). First
Now we are able to state the following theorem, which gives an effective finiteness result for the solutions of a so-called S-unit equation over function fields, which is
As already remarked we can prove similar results for arbitrary ground fields k when we assume corresponding results for the ℓ –rank of the class groups of quadratic extensions
Nous montrons que dans le cas r´egulier ( H = 1), elle est possible d`es que G poss`ede un sous-groupe d’ordre 6 et dans un r´ecent travail, Girstmair [6] vient de prouver que
I am very grateful to the anonymous referee for his valuable comments (incorporated into the current presentation as Re- marks 1–3), providing the proof of Lemma 5 and
Following the result of Feingold and Varga, a well-known theorem of Taussky on the eigenvalue distribution is extended to block diagonally dominant matrices and block H − matrices
