On Elliptic Curves in SL_2(C)/\Gamma, Schanuel's conjecture and geodesic lengths
Algebraic Geometry
2007-05-23 v3 Differential Geometry
Number Theory
Abstract
Let H be a discrete cocompact subgroup of SL_2(C). We conjecture that the quotient manifold X=SL_2(C)/H contains infinitely many non-isogeneous elliptic curves and prove that this is indeed the case if Schanuel's conjecture holds. We also prove it in the special case where the intersection of H and SL_2(R) is cocompact in SL_2(R). Furthermore, we deduce some consequences for the geodesic length spectra of real hyperbolic 2- and 3-folds.
Keywords
Cite
@article{arxiv.math/0204195,
title = {On Elliptic Curves in SL_2(C)/\Gamma, Schanuel's conjecture and geodesic lengths},
author = {Joerg Winkelmann},
journal= {arXiv preprint arXiv:math/0204195},
year = {2007}
}
Comments
20 pages; LaTeX; lemma 2 corrected, some minor improvements in presentation