On $3$-dimensional foliated dynamical systems and Hilbert type reciprocity law

Abstract

We show some fundamental results concerning $3$-dimensional foliated dynamical systems (FDS${}^3$ for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS${}^3$, which yields a classification of FDS${}^3$'s. Secondly, for each type of the classification, we construct concrete examples of FDS${}^3$'s. Finally, by using the integration theory for smooth Deligne cohomology, we introduce geometric analogues of local symbols and show a Hilbert type reciprocity law for an FDS${}^3$. Our results answer the question posed by Deninger.

30 pages, 3 figures

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• Number theory and dynamical systems on foliated spaces
• A dynamical systems analogue of Lichtenbaum's conjectures on special values of Hasse-Weil zeta functions
• Arithmetic Geometry and Analysis on Foliated Spaces
• Reeb components with complex leaves and their symmetries I : The automorphism groups and Schröder's equation on the half line

Cited by in corpus (2)

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