Mathematical Research Letters

Volume 21 (2014)

Number 4

The first $p$-jet space of an elliptic curve: global functions and lifts of Frobenius

Pages: 677 – 689



Alexandru Buium (Department of Mathematics and Statistics, University of New Mexico, Albuquerque, N.M., U.S.A.)

Arnab Saha (Mathematical Sciences Institute, Australian National University, Canberra, Australia)


We prove that there are no non-constant global functions and no lifts of Frobenius on the first $p$-jet space on an elliptic curve unless the elliptic curve itself has a lift of Frobenius.

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