Period-index and u-invariant questions for function fields over complete discretely valued fields
نویسندگان
چکیده
منابع مشابه
PERIOD-INDEX AND u-INVARIANT QUESTIONS FOR FUNCTION FIELDS OVER COMPLETE DISCRETELY VALUED FIELDS
Let K be a complete discretely valued field with residue field κ and F the function field of a curve over K. Let p be the characteristic of κ and l a prime not equal to p. If the Brauer l-dimensions of all finite extensions of κ are bounded by d and the Brauer l-dimensions of all extensions of κ of transcendence degree at most 1 are bounded by d + 1, then it is known that the Brauer l-dimension...
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Let K be a field with a valuation satisfying the following conditions: both K and the residue field k have characteristic zero; the value group is not 2-divisible; there exists a maximal subfield F in the valuation ring such that Gal(F̄ /F ) and Gal(k̄/k) have the same 2-cohomological dimension and this dimension is finite. Then Hilbert’s Tenth Problem has a negative answer for any function field...
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We prove equidistribution of a generic net of small points in a projective variety X over a function field K. For an algebraic dynamical system over K, we generalize this equidistribution theorem to a small generic net of subvarieties. For number fields, these results were proved by Yuan and we transfer here his methods to function fields. If X is a closed subvariety of an abelian variety, then...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2013
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-013-0483-y