TY - JOUR
T1 - Pesenti-Szpiro inequality for optimal elliptic curves
AU - Papikian, Mihran
N1 - Funding Information:
Part of the work on this paper was completed while the author was supported by a Rackham Predoc toral Fellowship from the University of Mic higan. E-mail address: [email protected].
PY - 2005/10
Y1 - 2005/10
N2 - We study Pesenti-Szpiro inequality in the case of elliptic curves over Fq(t) which occur as subvarieties of Jacobian varieties of Drinfeld modular curves. In general, we obtain an upper-bound on the degrees of minimal discriminants of such elliptic curves in terms of the degrees of their conductors and q. In the special case when the level is prime, we bound the degrees of discriminants only in terms of the degrees of conductors. As a preliminary step in the proof of this latter result we generalize a construction (due to Gekeler and Reversat) of 1-dimensional optimal quotients of Drinfeld Jacobians.
AB - We study Pesenti-Szpiro inequality in the case of elliptic curves over Fq(t) which occur as subvarieties of Jacobian varieties of Drinfeld modular curves. In general, we obtain an upper-bound on the degrees of minimal discriminants of such elliptic curves in terms of the degrees of their conductors and q. In the special case when the level is prime, we bound the degrees of discriminants only in terms of the degrees of conductors. As a preliminary step in the proof of this latter result we generalize a construction (due to Gekeler and Reversat) of 1-dimensional optimal quotients of Drinfeld Jacobians.
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U2 - 10.1016/j.jnt.2004.11.007
DO - 10.1016/j.jnt.2004.11.007
M3 - Article
AN - SCOPUS:24744437108
SN - 0022-314X
VL - 114
SP - 361
EP - 393
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -