Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cycle maps on cohomology theories for dg-categories and their
  applications   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 $X$, then they are equivalent to the classical
Tate and Hodge conjectures for $X$ respectively. We also propose a strategy of
how to prove these conjectures by utilizing a version of motivic Bass
conjecture.

9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org