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Holomorphic one-forms, integral and rational points on complex hyperbolic surfaces
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Sai-Kee Yeung
Published/Copyright:
January 8, 2013
Abstract
The first goal of this paper is to study the question of finiteness of integral points on a cofinite non-compact complex two-dimensional ball quotient defined over a number field. Along the process we will also consider some negatively curved compact surfaces. Using some fundamental results of Faltings, the question is to reduce to a conjecture of Borel about existence of virtual holomorphic one-forms on cofinite non-cocompact complex ball quotients. The second goal of this paper is to study the conjecture on such non-compact surfaces.
Funding source: National Science Foundation
Received: 2011-9-8
Published Online: 2013-1-8
Published in Print: 2014-12-1
© 2014 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Holomorphic one-forms, integral and rational points on complex hyperbolic surfaces
- Mordell–Weil groups of elliptic threefolds and the Alexander module of plane curves
- Reflexive differential forms on singular spaces. Geometry and cohomology
- Special cycles on unitary Shimura varieties II: Global theory
- Batalin–Vilkovisky structures on Ext and Tor
- Tangent cones and regularity of real hypersurfaces
Articles in the same Issue
- Frontmatter
- Holomorphic one-forms, integral and rational points on complex hyperbolic surfaces
- Mordell–Weil groups of elliptic threefolds and the Alexander module of plane curves
- Reflexive differential forms on singular spaces. Geometry and cohomology
- Special cycles on unitary Shimura varieties II: Global theory
- Batalin–Vilkovisky structures on Ext and Tor
- Tangent cones and regularity of real hypersurfaces
