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On the arithmetic of modular curves.

Ling, San.

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On the arithmetic of modular curves.

Record Type:	Electronic resources : Monograph/item
Title/Author:	On the arithmetic of modular curves./
Author:	Ling, San.
Description:	118 p.
Notes:	Source: Dissertation Abstracts International, Volume: 51-09, Section: B, page: 4382.
Contained By:	Dissertation Abstracts International51-09B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9103794

On the arithmetic of modular curves.
Ling, San.

On the arithmetic of modular curves. - 118 p.

Source: Dissertation Abstracts International, Volume: 51-09, Section: B, page: 4382.

Thesis (Ph.D.)--University of California, Berkeley, 1990.

We study an assortment of problems concerning the modular curves Subjects--Topical Terms:

515831
Mathematics.

On the arithmetic of modular curves.
LDR:02147nmm 2200253 4500 001 1861629
005 20041117065552.5
008 130614s1990 eng d
035 $a (UnM)AAI9103794
035 $a AAI9103794
040 $a UnM $c UnM
100 1 $a Ling, San. $3 1899528
245 1 0 $a On the arithmetic of modular curves.
300 $a 118 p.
500 $a Source: Dissertation Abstracts International, Volume: 51-09, Section: B, page: 4382.
500 $a Chairman: Ken Ribet.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 1990.
520 $a We study an assortment of problems concerning the modular curves $ and their Jacobians $. We first give a complete description of the Shimura subgroup $\ Sigma(N) $ of the Jacobian $ in terms of its group structure and the associated actions of Galois, of Atkin-Lehner involutions and of Hecke operators. We also determine the group structure of the Shimura subgroups in the Jacobians of Shimura curves. Next, we study the problem of finding congruence relations between cusp forms on $\ Gamma\sb0(p $) and $\ Gamma\sb0(p\sp2 $) , where $p $ is a prime. A classification theorem on the primes of fusion (i.e., the primes that give the desired congruence relations) is proved. We also show that the degeneracy maps from $) to $ give an isomorphism between the tori in the reduction modulo $p $ of $ and $. This is then used to show that the kernel (in characteristic 0) of the degeneracy map $ is the Shimura subgroup $\ Sigma(p $) , embedded antidiagonally in $. A theorem calculating the degree of the isogeny $ is also proved. We then carry out the calculations of the Fitting ideal of the group of F $\ sb{p\sp{n}} $- rational points of $ (where $q \ne p $ is a prime) in the Hecke algebra. Finally, we study the kernel of the degeneracy map $ by considering the restrictions of this map to the Shimura subgroups, cuspidal subgroups and a group $ defined by Mazur.
590 $a School code: 0028.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a University of California, Berkeley. $3 687832
773 0 $t Dissertation Abstracts International $g 51-09B.
790 1 0 $a Ribet, Ken, $e advisor
790 $a 0028
791 $a Ph.D.
792 $a 1990
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9103794