Universal torsors and values of quadratic polynomials represented by norms
U Derenthal, A Smeets, D Wei - Mathematische Annalen, 2015 - Springer
Let K/k K/k be an extension of number fields, and let P (t) P (t) be a quadratic polynomial
over k k. Let XX be the affine variety defined by P (t)= N_ K/k (z) P (t)= NK/k (z). We study the
Hasse principle and weak approximation for XX in three cases. For K: k= 4 K: k= 4 and P (t)
P (t) irreducible over kk and split in KK, we prove the Hasse principle and weak
approximation. For k= Q k= Q with arbitrary KK, we show that the Brauer-Manin obstruction
to the Hasse principle and weak approximation is the only one. For K: k= 4 K: k= 4 and P (t) …
over k k. Let XX be the affine variety defined by P (t)= N_ K/k (z) P (t)= NK/k (z). We study the
Hasse principle and weak approximation for XX in three cases. For K: k= 4 K: k= 4 and P (t)
P (t) irreducible over kk and split in KK, we prove the Hasse principle and weak
approximation. For k= Q k= Q with arbitrary KK, we show that the Brauer-Manin obstruction
to the Hasse principle and weak approximation is the only one. For K: k= 4 K: k= 4 and P (t) …
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