Abstract Motivated by Lang–Vojta's conjecture, we show that the set of dominant rational self-
maps of an algebraic variety over a number field with only finitely many rational points in any …

Abstract Let Γ⊂PU(1,n) be a lattice and S_Γ be the associated ball quotient. We prove that,
if S_Γ contains infinitely many maximal complex totally geodesic subvarieties, then Γ is …

The Chabauty--Kim method is a tool for finding the integral or rational points on varieties
over number fields via certain transcendental $ p $-adic analytic functions arising from …

We continue our study of integral points on moduli schemes by combining the method of
Faltings (Arakelov, Parsin, Szpiro) with modularity results and Masser-W\" ustholz isogeny …

The strategy of combining the method of Faltings (Arakelov, Paršin, Szpiro) with modularity
and Masser–Wüstholz isogeny estimates allows to explicitly bound the height and the …

Abstract The Chabauty–Kim method is a tool for finding the integral or rational points on
varieties over number fields via certain transcendental p-adic analytic functions arising from …

We continue our study of integral points on moduli schemes by combining the method of
Faltings (Arakelov, Paršin, Szpiro) with modularity results and Masser–Wüstholz isogeny …

The cohomology of an arithmetic congruence subgroup of a connected reductive algebraic
group defined over a number field is captured in the automorphic cohomology of that group …

arXiv:1910.06900v1 [math.NT] 15 Oct 2019 Page 1 arXiv:1910.06900v1 [math.NT] 15 Oct
2019 GROWTH OF COHOMOLOGY OF ARITHMETIC GROUPS AND THE STABLE TRACE …

We give upper bounds on limit multiplicities of certain nontempered representations of
unitary groups U (a, b), conditionally on the endoscopic classification of representations. Our …