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Arithmetic on Curves

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Elliptic Curves, Modular Forms and Cryptography

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Abstract

We intend to give a brief account of what is known or conjectured about the set C(Q) of rational points on a smooth projective absolutely connected curve C of genus g over Q. The idea is to show how the arithmetic properties of algebraic curves are governed by the familiar trichotomy: g = 0, g = 1, g ≥ 2. Only incidentally shall we mention fields other than Q and varieties other than curves.

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Author information

Authors and Affiliations

  1. Harish-Chandra Research Institute (Formerly Mehta Research Institute), Chhatnag Road, Jhusi, Allahabad, 211 019, India

    Chandan Singh Dalawat

Authors
  1. Chandan Singh Dalawat
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Editor information

Editors and Affiliations

  1. Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, 160 014, India

    Ashwani K. Bhandari

  2. Institute of Mathematical Sciences, C I T Campus, Taramani, Chennai, 600 113, India

    D. S. Nagaraj

  3. Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211 019, India

    B. Ramakrishnan

  4. School of Mathematics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Mumbai, 400 005, India

    T. N. Venkataramana

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© 2003 Hindustan Book Agency

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Dalawat, C.S. (2003). Arithmetic on Curves. In: Bhandari, A.K., Nagaraj, D.S., Ramakrishnan, B., Venkataramana, T.N. (eds) Elliptic Curves, Modular Forms and Cryptography. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-15-6_13

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