Abstract
Every elliptic curve E/ℂ admits an isomorphism ℂ*/qℤ ≅ E(ℂ) by complex analytic functions, and we have seen amply demonstrated in Chapter s I and II the importance of such uniformizations. In this chapter we are going to study uniformizations over other complete fields such as ℝ and finite extensions K/ℚ p . We begin in §1 with a brief review of the relevant formulas over ℂ, and then in §2 we use the complex uniformization to investigate elliptic curves over ℝ.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Silverman, J.H. (1994). Elliptic Curves over Complete Fields. In: Advanced Topics in the Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol 151. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0851-8_6
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0851-8_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94328-2
Online ISBN: 978-1-4612-0851-8
eBook Packages: Springer Book Archive