Abstract
Given a torsion section of a semistable elliptic surface we prove equidistribution results for the components of singular fibers which are hit by the section and for the root of unity (identifying the zero component withC) which is hit by the section in case the section hits the zero component
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
[AMRT]Ash, A, Mumford, D, Rapoport, M andTai Y,Smooth Compactifications of Locally Symmetric Varieties, Math Sci Press, Brookline, Mass 1975
[CP]Cox, D A andParry, W R, Torsion in elliptic curves overk(t), Compositio Math 41 (1980), 337–354
[KKMS]Kempf, G Knudsen, F Mumford, D andSaint Donat B,Toroidal Embeddings I,Lecture Notes in Math 339, Springer Verlag, Berlin-Heidel berg 1973
[K]Kodaira K, On compact analytic surfaces II, IIIAnn of Math 78 (1963), 1–40
[M]Miranda, R, Component numbers for torsion sections of semistable elliptic sur faces, inProceedings of the Conference on Classification of Algebraic Varieties L'Aquila, Italy, May 1992, Contemporary Math (to appear)
[MP]Miranda, R andPersson, U, Torsion groups of elliptic surfaces,Compositio Math 72 (1989), 249–267
[Shm]Shimura, G,Arithmetic Theory of Automorphic Functions, Princeton Univ Press, Princeton, N J, 1971
[Shd]Shioda, T, On elliptic modular surfaces,J Math Soc Japan 24 (1972), 20–59
[Sil]Silverman, J H,The Arithmetic Theory of Elliptic Curves Graduate Texts in Mathematics 106, Springer Verlag, New York-Berlin, 1986
Author information
Authors and Affiliations
Additional information
Research supported in part by the NSF under grant DMS 9104058 and the NSA under grant MDA 904-92 H 3022
Rights and permissions
About this article
Cite this article
Miranda, R., Stiller, P. Torsion sections of elliptic surfaces. Ark. Mat. 33, 117–134 (1995). https://doi.org/10.1007/BF02559607
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02559607