Weak Approximation for Tori Over p-adic Function Fields
نویسندگان
چکیده
منابع مشابه
WEAK 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 ...
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Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n ≥ 1 over k. Then Hilbert’s Tenth Problem for L is undecidable. In particular, Hilbert’s Tenth Problem for function fields of varieties over number fields of dimension ≥ 1 is undecidable.
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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...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2014
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnu019