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The index of an Eisenstein ideal and multiplicity one

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Title
The index of an Eisenstein ideal and multiplicity one
Author(s)
Hwajong Yoo
Publication Date
2016-04
Journal
MATHEMATISCHE ZEITSCHRIFT, v.282, no.3-4, pp.1097 - 1116
Publisher
SPRINGER
Abstract
Mazur’s fundamental work on the Eisenstein ideal of prime level has a variety of arithmetic applications. In this article, we generalize some of his work to square-free level. More specifically, we attempt to compute the index of an Eisenstein ideal and the dimension of the (Formula presented.) -torsion of the modular Jacobian variety, where (Formula presented.) is an Eisenstein maximal ideal. In many cases, the dimension of the (Formula presented.) -torsion is 2, in other words, a multiplicity one theorem holds. © 2015, Springer-Verlag Berlin Heidelberg
URI
https://pr.ibs.re.kr/handle/8788114/2587
ISSN
0025-5874
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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