English

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 XX, then they are equivalent to the classical Tate and Hodge conjectures for XX 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}
}