کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595163 1335801 2008 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Ihara's lemma for imaginary quadratic fields
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Ihara's lemma for imaginary quadratic fields
چکیده انگلیسی

An analogue over imaginary quadratic fields of a result in algebraic number theory known as Ihara's lemma is established. More precisely, we show that for a prime ideal p of the ring of integers of an imaginary quadratic field F, the kernel of the sum of the two standard p-degeneracy maps between the cuspidal sheaf cohomology is Eisenstein. Here Y0 and Y1 are analogues over F of the modular curves Y0(N) and Y0(Np), respectively. To prove our theorem we use the method of modular symbols and the congruence subgroup property for the group SL2(Z[1/p]) which is due to Mennicke [J. Mennicke, On Ihara's modular group, Invent. Math. 4 (1967) 202–228] and Serre [J.-P. Serre, Le problème des groupes de congruence pour SL2, Ann. of Math. (2) 92 (1970) 489–527].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 128, Issue 8, August 2008, Pages 2251-2262