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Reduction mod p and Torsion Points

  • Dale Husemöller
Part of the Graduate Texts in Mathematics book series (GTM, volume 111)

Abstract

Reduction modulo p defined ZZ/p Z = F p is a fundamental construction for studying equations in arithmetic. Another basic advantage of projective space over affine space is that the entire rational projective space can be reduced modulo p, P h (Q) → P n (F p ), in such a way that rational curves (curves defined over Q) and their intersection points also reduce modulo p. The first task is to study when the reduced curve is again smooth and when intersection multiplicities are preserved. This is an extension of the ideas in Chapter 2 to arithmetic.

Keywords

Normal Form Elliptic Curve Minimal Model Elliptic Curf Valuation Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Dale Husemöller
    • 1
  1. 1.Department of MathematicsHaverford CollegeHaverfordUSA

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