Rich representations and superrigidity
Algebraic Geometry
2025-07-09 v3 Dynamical Systems
Geometric Topology
Number Theory
Abstract
We investigate and compare applications of the Zilber-Pink conjecture and dynamical methods to rigidity problems for arithmetic real and complex hyperbolic lattices. Along the way we obtain new general results about reconstructing a variation of Hodge structure from its typical Hodge locus that may be of independent interest. Applications to Siu's immersion problem are also discussed, the most general of which only requires the hypothesis that infinitely many closed geodesics map to proper totally geodesic subvarieties under the immersion.
Cite
@article{arxiv.2402.03601,
title = {Rich representations and superrigidity},
author = {Gregorio Baldi and Nicholas Miller and Matthew Stover and Emmanuel Ullmo},
journal= {arXiv preprint arXiv:2402.03601},
year = {2025}
}
Comments
v2: Minor changes and improvements. v3: Final version to appear in Ergodic Theory Dynam. Systems