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to the weak approximation problem. V. E. Voskresenskii UDC 512,743 R-equivalence on the unimodular group of a simple algebra is studied in detail. A rather complete characterization is obtained for the R ...
), "On factorizable groups ." V. V. Kabanov (Sverdlovsk), "On finite groups with a self-centralizing subgroup of order 6." 295th Session. May 23, 1972 A. T. Gainov, "Finite-dimensional algebras with weak divisibility ...
uniformly believed [10]. We will not answer either of these questions, but we will relate them to another open question concerning the Brauer–Manin obstruction to weak approximation on Kummer varieties ...
the completion $${K}_{\nu}$$ at each place $$\nu$$ of $$K$$. This naturally leads to the study of local-global problems (i.e., weak approximation ) for $$X$$. The variety $$X$$ is said to satisfy weak approximation ...
that there are no transcendental obstructions to weak approximation on abelian varieties . The 2nd statement says that the locally constant (a fortiori algebraic ) Brauer classes on X capture the Brauer–Manin obstruction ...
defined in Definition 6.3. Our adaptation of Liang’s strategy to the case of (geometric) Kummer varieties also yields an analogous result for this notion of weak approximation : Theorem 1.4. Let |$W:=\prod ...
Friedlander and by Dennis Sullivan. More recently, people including Yonatan Harpaz, Ambrus Pál, and Tomer M. Schlank use it to study rational points of algebraic varieties . Associated to a locally noetherian ...
in the family fail weak approximation and almost all also have no Brauer–Manin obstruction to the Hasse principle. These results do not apply here as they concern smooth projective varieties . But a similar method ...
\rangle\! \rangle _\Delta$| associated to |$\Delta$|, which comes with certain distinguished elements |$z_1, \dots , z_N$|. This algebra is approximately a completion of the group ring of |$H_1(L; \mathbb ...
of cycles homologically equivalent to zero modulo a potentially weaker relation , called algebraic equivalence. More recently, Totaro showed that the Griffiths group of a complex variety can be analyzed using ...
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