Cycle maps on cohomology theories for dg-categories and their applications

Satoshi Mochizuki

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arXiv · 2002.04373

Cycle maps on cohomology theories for dg-categories and their applications

Satoshi Mochizuki

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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 $X$, 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.

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BibTeX RIS

Satoshi Mochizuki. 2020-02-11. Cycle maps on cohomology theories for dg-categories and their applications. https://arxiv.org/abs/2002.04373

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