Israel Journal of Mathematics

, Volume 202, Issue 1, pp 275–293 | Cite as

Hasse principle and weak approximation for multinorm equations

Article

Abstract

In this note, we are interested in local-global principles for multinorm equations \(\prod\nolimits_{i = 1}^n {{N_{{L_i}/k}}({z_i}} ) = a\) where k is a global field, Li/k are finite separable field extensions and ak*.

In particular, we prove a result relating the Hasse principle and weak approximation for this equation to the Hasse principle and weak approximation for some classical norm equation NF/k(w) = a where \(F: = \bigcap\nolimits_{i = 1}^n {{L_i}} \). It provides a proof of a “weak approximation” analogue of a recent conjecture by Pollio and Rapinchuk about the multinorm principle. We also provide a counterexample to the original conjecture concerning the Hasse principle.

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Copyright information

© Hebrew University of Jerusalem 2014

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Academy of Mathematics and System ScienceCASBeijingP. R. China
  3. 3.Mathematisches Institut der Universität MünchenMünchenGermany

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