Algebra Seminar: Hasse principle over function fields of p-adic curves

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Raman Parimala, Emory University Title: Hasse principle over function fields of p-adic curves Abstract: Let F be the function field of a p-adic curve. We discuss Hasse principle for homogeneous spaces under connected linear algebraic groups defined over F with respect to its discrete valuations. Many classical results familiar in the context of number fields are true in the setting of function fields. We discuss some open conjectures and recent progress on Hasse principle over such fields.