Weak approximation over function fields
نویسندگان
چکیده
منابع مشابه
Weak Approximation over Function Fields
— We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.
متن کاملWeak Approximation and R-equivalence over Function Fields of Curves
For a rationally connected fibration over a complex curve, and for a closed point of the curve, we prove that every power series section of the fibration near the point is approximated to arbitrary order by polynomial sections provided the “Laurent fiber”, i.e., the deleted power series neighborhood of the fiber, as a variety over the Laurent series field is R-connected – the analogue of ration...
متن کاملWEAK APPROXIMATION FOR TORI OVER p-ADIC FUNCTION FIELDS
We study local-global questions for Galois cohomology over the function field of a curve defined over a p-adic field, the main focus being weak approximation of rational points. We construct a 9-term Poitou–Tate type exact sequence for tori over a field as above (and also a 12-term sequence for finite modules). Like in the number field case, part of the sequence can then be used to analyze the ...
متن کاملWeak Approximation over Function Fields of Curves over Large or Finite Fields
Let K = k(C) be the function field of a curve over a field k and let X be a smooth, projective, separably rationally connected K-variety with X(K) 6= ∅. Under the assumption that X admits a smooth projective model π : X → C, we prove the following weak approximation results: (1) if k is a large field, then X(K) is Zariski dense; (2) if k is an infinite algebraic extension of a finite field, the...
متن کاملA Local-global Principle for Weak Approximation on Varieties over Function Fields
We present a new perspective on the weak approximation conjecture of Hassett and Tschinkel: formal sections of a rationally connected fibration over a curve can be approximated to arbitrary order by regular sections. The new approach involves the study of how ideal sheaves pullback to Cartier divisors. 1. Statement of results Disclaimer. This is the first draft of an article which was circulate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2005
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-005-0458-8