English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

It is a theorem of Ribet that an abelian variety defined over a number field   $K$   has only finitely many torsion points with values in the maximal cyclotomic extension field   $K^{\textrm{cyc}}$   of   $K$  . Recently, Rössler and Szamuely generalized Ribet’s theorem in terms of the étale cohomology with   $\mathbb{Q}/\mathbb{Z}$  -coefficients of a smooth proper variety. In this paper, we show that the same finiteness holds even after replacing   $K^{\textrm{cyc}}$   with the field obtained by adjoining to   $K$   all roots of all elements of a certain subset of   $K$  . Furthermore, we give some new examples of TKND-AVKF fields; the notion of TKND-AVKF is introduced by Hoshi, Mochizuki, and Tsujimura. Also, TKND-AVKF fields are expected as one of suitable base fields for anabelian geometry.

Some Kummer Extensions Over Maximal Cyclotomic Fields, a Finiteness Theorem of Ribet and TKND-AVKF Fields