Isotropy of quadratic forms over function fields of $p$-adic curves

R. Parimala; V. Suresh

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In the previous paper [15], we determined the structure of the Galois groups $Gal (K_{u r} / K)$ of the maximal unramified extensions $K_{u r}$ of imaginary quadratic number fields $K$ of conductors $≦ 1000$ under the Generalized Riemann Hypothesis (GRH) except for 23 fields (these are of conductors $≧ 723$ ) and give a table of $Gal (K_{u r} / K)$ . We update the table (under GRH). For 19 exceptional fields $K$ of them, we determine $Gal (K_{u r} / K)$ . In particular, for $K = 𝐐 (\sqrt{- 856})$ , we obtain $Gal (K_{u r} / K) ≅ \tilde{S_{4}} \times C_{5} and K_{u r} = K_{4}$ , the fourth Hilbert class field of $K$ . This is the first example of a number...

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Displaying similar documents to “Isotropy of quadratic forms over function fields of p -adic curves”

Displaying similar documents to “Isotropy of quadratic forms over function fields of $p$ -adic curves”