The Andre-Oort conjecture
Bruno Klingler, Andrei Yafaev
TL;DR
This paper proves the Andre-Oort conjecture for Shimura varieties assuming the Generalized Riemann Hypothesis, and unconditionally for certain cases, advancing understanding of special points in algebraic geometry.
Contribution
It establishes the Andre-Oort conjecture under GRH and proves it unconditionally for specific cases, marking significant progress in the field.
Findings
Proves the conjecture assuming GRH.
Unconditional proof for special cases.
Enhances understanding of special points in Shimura varieties.
Abstract
In this paper we prove, assuming the Generalized Riemann Hypothesis, the Andr?e-Oort conjecture on the Zariski closure of sets of special points in a Shimura variety. In the case of sets of special points satisfying an additional assumption, we prove the conjecture without assuming the GRH.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Analytic Number Theory Research