Hasse principles and the u-invariant over formally real 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...
متن کاملCurves over Global Fields Violating the Hasse Principle
We exhibit for each global field k an algebraic curve over k which violates the Hasse Principle. We can find such examples among Atkin-Lehner twists of certain elliptic modular curves and Drinfeld modular curves. Our main tool is a refinement of the “Twist Anti-Hasse Principle” (TAHP). We then use TAHP to construct further Hasse Principle violations, e.g. among curves over any number field of a...
متن کاملCurves over Finite Fields Attaining the Hasse-Weil Upper Bound
Curves over finite fields (whose cardinality is a square) attaining the Hasse-Weil upper bound for the number of rational points are called maximal curves. Here we deal with three problems on maximal curves: 1. Determination of the possible genera of maximal curves. 2. Determination of explicit equations for maximal curves. 3. Classification of maximal curves having a fixed genus.
متن کاملA Hasse Principle for Quadratic Forms over Function Fields
We describe the classical Hasse principle for the existence of nontrivial zeros for quadratic forms over number fields, namely, local zeros over all completions at places of the number field imply nontrivial zeros over the number field itself. We then go on to explain more general questions related to the Hasse principle for nontrivial zeros of quadratic forms over function fields, with referen...
متن کاملHasse principle for Classical groups over function fields of curves over number fields
In ([CT]), Colliot-Thélène conjectures the following: Let F be a function field in one variable over a number field, with field of constants k and G be a semisimple simply connected linear algebraic group defined over F . Then the map H(F,G) → ∏ v∈Ωk H(Fv, G) has trivial kernel, Ωk denoting the set of places of k. The conjecture is true if G is of type A, i.e., isomorphic to SL1(A) for a centra...
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: Nagoya Mathematical Journal
سال: 1976
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000017347