The action of the hecke operators on the component groups of modular jacobian varieties

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Title
The action of the hecke operators on the component groups of modular jacobian varieties
Author(s)
TAEKYUNG KIM; HWAJONG YOO
Publication Date
2018-08
Journal
Pacific Journal of Mathematics, v.296, no.2, pp.341 - 355
Publisher
Mathematical Sciences Publishers
Abstract
For a prime number q≥5 and a positive integer N prime to q, Ribet proved the action of the Hecke algebra on the component group of the Jacobian variety of the modular curve of level Nq at q is Eisenstein, which means the Hecke operator Tℓ acts by ℓ C 1 when ℓ is a prime number not dividing the level. We completely compute the action of the Hecke algebra on this component group by a careful study of supersingular points with extra automorphisms. © 2018 Mathematical Sciences Publishers
URI
https://pr.ibs.re.kr/handle/8788114/4939
ISSN
0030-8730
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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