On unstable cohomology classes of SL(Z).
نویسنده
چکیده
From algebraic K-theory, we show that there exists a spectral sequence that has real cohomology of SL(n)(Z) as its E(1)-terms and converges to the tensor product of a polynomial algebra and an exterior algebra. On the basis of this spectral sequence, we discovered several families of real unstable cohomology classes of SL(n)(Z).
منابع مشابه
Cohomology 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 کاملGalois Representations Attached to Tensor Products of Arithmetic Cohomology
We compute the action of Hecke operators on tensor products of cohomology classes of lower congruence subgroups of SL(n,Z) in trivial weight. We use this computation to prove that if each representation in a collection of Galois representations is attached to a cohomology class of a lower congruence subgroup in trivial weight, then a sum of certain twists of the representations consistent with ...
متن کاملGalois Representations Attached to Tensor Products of Arithmetic Cohomology Avner Ash and Darrin Doud
We compute the action of Hecke operators on tensor products of cohomology classes of lower congruence subgroups of SL(n,Z) in trivial weight. We use this computation to prove that if each representation in a collection of Galois representations is attached to a cohomology class of a lower congruence subgroup in trivial weight, then a sum of certain twists of the representations consistent with ...
متن کاملHorn recursion for a new product in the cohomology of partial flag varieties SL
Let G be a connected semi-simple complex algebraic group and let P be a standard parabolic subgroup and consider the homogeneous spaceG/P . IfW is the Weyl group ofG, letW P be the set of minimal length representatives of the coset spaceW/WP . For any w ∈ W P , define [Λ̄w] to be the cohomology class of the shifted Schubert variety Λ̄w := w−1BwP ⊆ G/P . It is well known that the elements of W P p...
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
عنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 75 1 شماره
صفحات -
تاریخ انتشار 1978