``Shafarevich-Tate sets'' for profinite groups
نویسندگان
چکیده
منابع مشابه
Tate-Shafarevich groups and K3 surfaces
This paper explores a topic taken up recently by Logan and van Luijk, finding nontrivial 2-torsion elements of the Tate-Shafarevich group of the Jacobian of a genus-2 curve by exhibiting Brauer-Manin obstructions to rational points on certain quotients of principal homogeneous spaces of the Jacobian, whose desingularizations are explicit K3 surfaces. The main difference between the methods used...
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Around 1940, Lind [Lin] and (independently, but shortly later) Reichardt [Re] discovered that some genus 1 curves over Q, such as 2y = 1− 17x, violate the Hasse principle; i.e., there exist x, y ∈ R satisfying the equation, and for each prime p there exist x, y ∈ Qp satisfying the equation, but there do not exist x, y ∈ Q satisfying the equation. In fact, even the projective nonsingular model h...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1999
ISSN: 0386-2194
DOI: 10.3792/pjaa.75.96