44 research outputs found
On volumes of arithmetic quotients of PO(n,1), n odd
We determine the minimal volume of arithmetic hyperbolic orientable
n-dimensional orbifolds (compact and non-compact) for every odd dimension n>3.
Combined with the previously known results it solves the minimal volume problem
for arithmetic hyperbolic n-orbifolds in all dimensions.Comment: 34 pages, final revision, to appear in Proc. LM
Manifolds counting and class field towers
In [BGLM] and [GLNP] it was conjectured that if is a simple Lie group of
real rank at least 2, then the number of conjugacy classes of (arithmetic)
lattices in of covolume at most is where is an explicit constant computable from the (absolute)
root system of . In this paper we prove that this conjecture is false. In
fact, we show that the growth is at rate . A crucial ingredient of
the proof is the existence of towers of field extensions with bounded root
discriminant which follows from the seminal work of Golod and Shafarevich on
class field towers.Comment: 27 pages, a small change in title, final revision, to appear in Adv.
Mat