Linear independence in linear systems on elliptic curves

  • Bradley W. Brock

    Center for Communications Research, Princeton, USA
  • Bruce W. Jordan

    Baruch College, CUNY, New York, USA
  • Bjorn Poonen

    Massachusetts Institute of Technology, Cambridge, USA
  • Anthony J. Scholl

    University of Cambridge, UK
  • Joseph L. Wetherell

    Center for Communications Research, San Diego, USA
Linear independence in linear systems on elliptic curves cover
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Abstract

Let be an elliptic curve, with identity , and let be a cyclic subgroup of odd order , over an algebraically closed field with char . For , let be a rational function with divisor . We ask whether the functions are linearly independent. For generic , we prove that the answer is yes. We bound the number of exceptional when is a prime by using the geometry of the universal generalized elliptic curve over . The problem can be recast in terms of sections of an arbitrary degree line bundle on .

Cite this article

Bradley W. Brock, Bruce W. Jordan, Bjorn Poonen, Anthony J. Scholl, Joseph L. Wetherell, Linear independence in linear systems on elliptic curves. Comment. Math. Helv. 96 (2021), no. 2, pp. 199–213

DOI 10.4171/CMH/511