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By Wang X.

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Then C ∗ E(R)• ∗ ∼ = k i (C ⊕ ˇaR R ) →C , i=1 proving the lemma. 5 The space of automorphic forms It is known that H ∗ (G, C) can be evaluated by using the cohomology of the de Rham complex, which is isomorphic to the standard complex for evaluating ∗ (C ∞ (AG (R)+ G(Q)\G(A))). 1) be the subspace of functions of uniformly moderate growth. Let J = U(g)g ∩ Z(g) be the annihilator of the constant representation in Z(g). Let ∞ (AG (R)+ G(Q)\G(A)) J n f = {0} for n AJ : = f ∈ Cumg 0 . 1) defines an isomorphism on coho∞ also defines an isomology and conjectured that the inclusion AJ ⊂ Cumg morphism on cohomology with constant coefficients.

Ecole Norm. Sup. (4) 2 (1969), p. 1–62. de Summary. We construct a topological model for certain Eisenstein cohomology of congruence subgroups. 1 Introduction Let G be a semisimple algebraic group over Q, let G(Q) and G(A) be its rational and adelic groups, and let K ⊂ G(A) be a good maximal compact subgroup. Let K = K f K ∞ with K ∞ ⊂ G(R) and K f ⊂ G(Af ), where G(Af ) is the finite adelic group and G(R) is the group of real points. By our assumption on G, we know that G(R) and K ∞ are connected Lie groups (cf.

Let IS be the ideal f ∈ HS IS : = f (g) dg = 0 , G(AS ) and let H ∗ (G, C)I : = {x ∈ H ∗ (G, C) |for any set S of finite primes, ISm x = {0} for m 0} Hc∗ (G, C)I : = {x ∈ Hc∗ (G, C) |for 0} . any set S of finite primes, ISm x = {0} for m These are direct summands of H ∗ (G, C) and Hc∗ (G, C). Our main result describes them as the space of K o∞ ∩ Po (R)-invariants in the hypercohomology of a complex of sheaves of G(Af )-modules on the compact dual. The construction of these complexes of sheaves follows a general pattern, which associates a chain complex to a functor with values in an abelian category on the poset PG of standard parabolic subgroups.

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2-dimensional simple factors of J 0(N) by Wang X.


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