Linear independence in linear systems on elliptic curves
Bradley W. Brock
Center for Communications Research, Princeton, USABruce W. Jordan
Baruch College, CUNY, New York, USABjorn Poonen
Massachusetts Institute of Technology, Cambridge, USAAnthony J. Scholl
University of Cambridge, UKJoseph L. Wetherell
Center for Communications Research, San Diego, USA
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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