Elliptic Curves over Complete Fields
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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.
KeywordsPower Series Exact Sequence Elliptic Curve Elliptic Curf Formal Power Series
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