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On Elliptic Curves in SL2(ℂ)/Γ.., Schanuel’s Conjecture and Geodesic Lengths
Published online by Cambridge University Press: 22 January 2016
Abstract
Let Γ be a discrete cocompact subgroup of SL2(ℂ). We conjecture that the quotient manifold X = SL2(ℂ) / Γ contains infinitely many non-isogenous elliptic curves and prove this is indeed the case if Schanuel’s conjecture holds. We also prove it in the special case where Γ ∩ SL2(∝) is cocompact in SL2(ℝ).
Furthermore, we deduce some consequences for the geodesic length spectra of real hyperbolic 2- and 3-folds.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2004
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