A Variational Tate Conjecture in crystalline cohomology

• Published in: arXiv.org
• Main Author: Morrow, Matthew
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 25.03.2015
• Subjects: Crystal structure; Crystallinity; Fields (mathematics); Homology

Given a smooth, proper family of varieties in characteristic \(p>0\), and a cycle \(z\) on a fibre of the family, we formulate a Variational Tate Conjecture characterising, in terms of the crystalline cycle class of \(z\), whether \(z\) extends cohomologically to the entire family. This is a char...