Cycle maps on cohomology theories for dg-categories and their applications
Algebraic Geometry
2020-02-12 v1
Abstract
In this article, we propose noncommutative versions of Tate conjecture and Hodge conjecture. If we consider these conjectures for a dg-category of perfect complexes over a certain schemes , then they are equivalent to the classical Tate and Hodge conjectures for respectively. We also propose a strategy of how to prove these conjectures by utilizing a version of motivic Bass conjecture.
Keywords
Cite
@article{arxiv.2002.04373,
title = {Cycle maps on cohomology theories for dg-categories and their applications},
author = {Satoshi Mochizuki},
journal= {arXiv preprint arXiv:2002.04373},
year = {2020}
}