1 September 2019 Arithmetic of double torus quotients and the distribution of periodic torus orbits
Ilya Khayutin
Duke Math. J. 168(12): 2365-2432 (1 September 2019). DOI: 10.1215/00127094-2019-0016


We describe new arithmetic invariants for pairs of torus orbits on groups isogenous to an inner form of PGLn over a number field. These invariants are constructed by studying the double quotient of a linear algebraic group by a maximal torus.

Using the new invariants we significantly strengthen results toward the equidistribution of packets of periodic torus orbits on higher rank S-arithmetic quotients. Packets of periodic torus orbits are natural collections of torus orbits coming from a single adèlic torus and are closely related to class groups of number fields. The distribution of these orbits is akin to the distribution of integral points on homogeneous algebraic varieties with a torus stabilizer. The proof combines geometric invariant theory, Galois actions, local arithmetic estimates, and homogeneous dynamics.


Download Citation

Ilya Khayutin. "Arithmetic of double torus quotients and the distribution of periodic torus orbits." Duke Math. J. 168 (12) 2365 - 2432, 1 September 2019. https://doi.org/10.1215/00127094-2019-0016


Received: 18 May 2017; Revised: 17 February 2019; Published: 1 September 2019
First available in Project Euclid: 24 August 2019

zbMATH: 07145004
MathSciNet: MR3999448
Digital Object Identifier: 10.1215/00127094-2019-0016

Primary: 37A17
Secondary: 11F23

Keywords: Entropy , periodic orbit , Torus

Rights: Copyright © 2019 Duke University Press


This article is only available to subscribers.
It is not available for individual sale.

Vol.168 • No. 12 • 1 September 2019
Back to Top