Rank gain of Jacobian varieties over finite Galois extensions

Let K be a number field, and let X -> P-K(1) be a degree p covering branched only at 0, 1, and infinity. If K is a field containing a primitive p-th root of unity then the covering of P-1 is Galois over K, and if p is congruent to 1 mod 6, then there is an automorphism sigma of X which cyclically permutes the branch points. Under these assumptions, we show that the Jacobian of both X and X/<sigma > gain rank over infinitely many linearly disjoint cyclic degree p-extensions of K. We also show the existence of an infinite family of elliptic curves whose j-invariants are parametrized by a modular function on Gamma(0)(3) and that gain rank over infinitely many cyclic degree 3-extensions of Q.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2018-03
Language
English
Article Type
Article
Keywords

CURVES

Citation

JOURNAL OF NUMBER THEORY, v.184, pp.68 - 84

ISSN
0022-314X
DOI
10.1016/j.jnt.2017.08.010
URI
http://hdl.handle.net/10203/237144
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
  • Hit : 2831
  • Download : 0
  • Cited 0 times in thomson ci
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡClick to seewebofscience_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0