Computations of cuspidal cohomology of congruence subgroups of SL(3, Z)
نویسندگان
چکیده
منابع مشابه
Cuspidal Cohomology for Principal Congruence Subgroups of Gl(3, Z)
The cohomology of arithmetic groups is made up of two pieces, the cuspidal and noncuspidal parts. Within the cuspidal cohomology is a subspace— the /-cuspidal cohomology—spanned by the classes that generate representations of the associated finite Lie group which are cuspidal in the sense of finite Lie group theory. Few concrete examples of /-cuspidal cohomology have been computed geometrically...
متن کاملA Construction of Rigid Analytic Cohomology Classes for Congruence Subgroups of SL3(Z)
We give a constructive proof, in the special case of GL3, of a theorem of Ash and Stevens which compares overconvergent cohomology to classical cohomology. Namely, we show that every ordinary classical Hecke-eigenclass can be lifted uniquely to a rigid analytic eigenclass. Our basic method builds on the ideas of M. Greenberg; we first form an arbitrary lift of the classical eigenclass to a dist...
متن کاملCohomology of congruence subgroups of SL(4,Z) II
In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4(Z), J. Number Theory 94 (2002) 181–212] we computed cohomology groups H (Γ0(N),C), where Γ0(N) is a certain congruence subgroup of SL(4,Z), for a range of levels N . In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and addi...
متن کاملCohomology of Congruence Subgroups of Sl4(z). Iii
In two previous papers [AGM02,AGM08] we computed cohomology groups H(Γ0(N);C) for a range of levels N , where Γ0(N) is the congruence subgroup of SL4(Z) consisting of all matrices with bottom row congruent to (0, 0, 0, ∗) mod N . In this note we update this earlier work by carrying it out for prime levels up to N = 211. This requires new methods in sparse matrix reduction, which are the main fo...
متن کامل0 Cohomology of Congruence Subgroups of Sl 4 ( Z
Let N > 1 be an integer, and let Γ = Γ0(N) ⊂ SL4(Z) be the subgroup of matrices with bottom row congruent to (0, 0, 0, ∗) mod N . We compute H(Γ;C) for a range of N , and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the Borel-Serre compactification, to Eisenstein series, and to classical holomorphic modu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1984
ISSN: 0022-314X
DOI: 10.1016/0022-314x(84)90081-7