ON THE DISCRIMINANT OF A HYPERELLIPTIC CURVE

Authors
LOCKHART P
Citation
P. Lockhart, ON THE DISCRIMINANT OF A HYPERELLIPTIC CURVE, Transactions of the American Mathematical Society, 342(2), 1994, pp. 729-752
Citations number
17
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
342
Issue
2
Year of publication
1994
Pages
729 - 752
Database
ISI
SICI code
0002-9947(1994)342:2<729:OTDOAH>2.0.ZU;2-X
Abstract
The minimal discriminant of a hyperelliptic curve is defined and used to generalize much of the arithmetic theory of elliptic curves. Over n umber fieldS this leads to a higher genus version of Szpiro's Conjectu re. Analytically, the discriminant is shown to be related to Siegel mo dular forms of higher degree.