报告题目: Higher Eisenstein elements, higher Eichler formulas and rank of Heck algebras
报告人：Emmanuel LECOUTURIER（巴黎高师）
时间：2017年10月30日（星期一），9：30-11：30
地点： 管理科研楼1318教室
摘要：In his classical work, Mazur considered the Eisenstein ideal I of the Hecke algebar T acting on cusps forms of weight 2 and prime level N. The compeltion of T at the maximal ideal generated by I and an Eisenstein prime p is a Z_p-algebra of finite rank g_p as a Z_p-module. Mazur asked what can be said about this rank g_p. Merel gave a congruence criterion for g_p no smaller than 2.
In this talk, we shall give a congruence criterion for g_p no smaller than 3 and a more complicated criterion for g_p no smaller than 4. We also prove higher Eichler formulas in the talk. The proof of these resuts are based on the theory of higher Eisenstein elements. We consider several Hecke modules in our work and compute explicitly some higher Eisenstein elements in these modules.
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