@article{1d15a2ea975b45c3a61e53f55a765863,
title = "Anabelian geometry and descent obstructions on moduli spaces",
abstract = "We study the section conjecture of anabelian geometry and the sufficiency of the finite descent obstruction to the Hasse principle for the moduli spaces of principally polarized abelian varieties and of curves over number fields. For the former we show that the section conjecture fails and the finite descent obstruction holds for a general class of adelic points, assuming several well-known conjectures. This is done by relating the problem to a local-global principle for Galois representations. For the latter, we show how the sufficiency of the finite descent obstruction implies the same for all hyperbolic curves.",
author = "Stefan Patrikis and Voloch, {Jos{\'e} Felipe} and Zarhin, {Yuri G.}",
note = "Funding Information: Voloch would like to thank J. Achter, D. Harari, E. Ozman, T. Schlank, and J. Starr for comments and information. He would also like to thank the Simons Foundation (grant #234591) and the Centre Bernoulli at EPFL for financial support. Zarhin is grateful to Frans Oort, Ching-Li Chai and Jiangwei Xue for helpful discussions and to the Simons Foundation for financial and moral support (via grant #246625 to Yuri Zarkhin). Part of this work was done in May-June 2015 when he was visiting Department of Mathematics of the Weizmann Institute of Science (Rehovot, Israel). The final version of this paper was prepared in May-June 2016 when he was a visitor at the Max-Planck-Institut f{\"u}r Mathematik (Bonn, Germany). The hospitality and support of both institutes is gratefully acknowledged. We are very grateful to the anonymous referees, whose careful readings and comments have greatly improved the readability of this paper. We would also like to thank W. Sawin for comments. Publisher Copyright: {\textcopyright} 2016 Mathematical Sciences Publishers.",
year = "2016",
doi = "10.2140/ant.2016.10.1191",
language = "English (US)",
volume = "10",
pages = "1191--1219",
journal = "Algebra and Number Theory",
issn = "1937-0652",
publisher = "Mathematical Sciences Publishers",
number = "6",
}