Spaces of Sections of Quadric Surface Fibrations over Curves
نویسنده
چکیده
Let k be a field of characteristic not equal to two, B a smooth projective curve of genus g(B) over k, and F its function field. A quadric hypersurface fibration is a flat projective morphism π : X → B such that each geometric fiber is a quadric hypersurface with at worst an isolated singularity and the generic fiber is smooth. Sections σ : B → X of π are in bijection with rational points X(F ). Our study is motivated by arithmetic applications and analogies between function fields of curves and number fields. When k is a finite field, the following problems have been studied by various research groups:
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