Cohomology and torsion cycles over the maximal cyclotomic extension

Author: 

Rössler, D
Szamuely, T

Publication Date: 

1 July 2019

Journal: 

Journal für die Reine und Angewandte Mathematik (Crelle's Journal)

Last Updated: 

2020-01-21T16:06:04.607+00:00

abstract: 

A classical theorem by K. Ribet asserts that an abelian variety defined over
the maximal cyclotomic extension $K$ of a number field has only finitely many
torsion points. We show that this statement can be viewed as a particular case
of a much more general one, namely that the absolute Galois group of $K$ acts
with finitely many fixed points on the \'etale cohomology with $\bf Q/\bf
Z$-coefficients of a smooth proper $\overline K$-variety defined over $K$. We
also present a conjectural generalization of Ribet's theorem to torsion cycles
of higher codimension. We offer supporting evidence for the conjecture in
codimension 2, as well as an analogue in positive characteristic.

Symplectic id: 

745065

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Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article