Oberseminar Modular Curves and the Eisenstein Ideal Sommersemester 2010
نویسندگان
چکیده
Our main subject is to study the action of the Hecke operators Tl on the Jacobian J of the modular curve X0(N). We consider the Hecke algebra T, i.e. the subring of End(J) generated by the Tl and the involution ω and define the Eisenstein ideal I ⊂ T as the ideal generated by 1 +ω and 1 + l−Tl, l prime 6= N . The Eisenstein quotient of J is the quotient J̃ := J/aJ where a denotes the kernel of the natural map from T to the I-adic completion TI . A crucial step in the proof will be to show that the following
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