Abstract
Complex uniformization of curves is a popular tool in Number Theory. There are, however, some arithmetic and computational advantages in the use of p-adic uniformization. This paper compares the two theories and discusses how they can be used to study isogenies, with explicit examples of p-adic uniformization of hyperelliptic curves.
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Bosch, S., Güntzer, U., Remmert, R.: Non-Archimedean Analysis. Springer, Berlin (1984)
Darmon, H.: Rational Points on Modular Elliptic Curves. CBMS, vol. 101. Published for the Conference Board of the Mathematical Sciences, Washington (2004)
Diamond, F., Shurman, J.: A First Course in Modular Forms. Springer, New York (2005)
Fresnel, J., van der Put, M.: Analytic Geometry and Its Applications. Birkhäuser, Boston (2004)
Gerritzen, L.: Über Endomorphismen nichtarchimedischer holomorpher Tori. Invent. Math. 11, 27–36 (1970)
Gerritzen, L.: On non-Archimedean representations of abelian varieties. Math. Ann. 169, 323–346 (1972)
Gerritzen, L., van der Put, M.: Schottky Groups and Mumford Curves. Springer, Berlin (1980)
Serre, J.-P.: Abelian l-Adic Representations and Elliptic Curves. AK Peters, Wellesley (1998)
Tate, J.: Rigid analytic spaces. Invent. Math. 12, 257–289 (1971)
van Wamelen, P.: Poonen’s question concerning isogenies between smart’s genus 2 curves. Math. Comput. 69(232), 1685–1697 (2000)
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Kadziela, S. Rigid Analytic Uniformization of Curves and the Study of Isogenies. Acta Appl Math 99, 185–204 (2007). https://doi.org/10.1007/s10440-007-9162-6
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DOI: https://doi.org/10.1007/s10440-007-9162-6