Twisted fermat

Let p be a prime number, F a totally real field such that [F (µp ) : F ] = 2 and [F : Q] is odd. For δ ∈ F × , let [ δ ] denote its class in F × /F ×p . In this paper, we show Main Theorem. There are infinitely many classes [ δ ] ∈ F × /F ×p such that the twisted affine Fermat curves Wδ : have no F -rational points. Remark. It is clear that if [ δ ] = [ δ ], then Wδ is isomorphic to Wδ over F . For any δ ∈ F × , Wδ /F has rational points locally everywhere.

25p noel_noel 17-01-2013 46 7   Download