On descending cohomology geometrically
Algebraic Geometry
2019-02-20 v3 Number Theory
Abstract
In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an abelian variety, provided the geometric coniveau is maximal. This provides an affirmative answer to Mazur's question for all uni-ruled threefolds, for instance. Concerning cohomology in degree three, we show that the image of the Abel--Jacobi map admits a distinguished model over the rationals.
Keywords
Cite
@article{arxiv.1410.5376,
title = {On descending cohomology geometrically},
author = {Jeff Achter and Sebastian Casalaina-Martin and Charles Vial},
journal= {arXiv preprint arXiv:1410.5376},
year = {2019}
}
Comments
30 pages, AMS LaTeX, shortened exposition, some results strengthened. To appear in Composito Math. Material from appendix is now in arxiv:1610.06586; results on quadrics will appear elsewhere