On the equation N_{K/k}(\Xi)=P(t)
Number Theory
2014-06-09 v3
Abstract
For varieties given by an equation N_{K/k}(\Xi)=P(t), where N_{K/k} is the norm form attached to a field extension K/k and P(t) in k[t] is a polynomial, three topics have been investigated: (1) computation of the unramified Brauer group of such varieties over arbitrary fields; (2) rational points and Brauer-Manin obstruction over number fields (under Schinzel's hypothesis); (3) zero-cycles and Brauer-Manin obstruction over number fields. In this paper, we produce new results in each of three directions. We obtain quite general results under the assumption that K/k is abelian (as opposed to cyclic in earlier investigation).
Cite
@article{arxiv.1202.4115,
title = {On the equation N_{K/k}(\Xi)=P(t)},
author = {Dasheng Wei},
journal= {arXiv preprint arXiv:1202.4115},
year = {2014}
}
Comments
34 pages, Theorem 3.5 is generalized to any prime p (not only p=3). Proc. London Math. Soc. (to appear)