Abstract
AbstractLet F be a totally real number field and let E|F be a cyclic Galois extension with Galois group generated by σ. Let G0|F be a connected semi simple algebraic group defined over F, put G = res ℚ(G0 x FE) and assume that G0(F ⊗ ℝ) contains a compact Cartan. Let Y be the locally symmetric space which is determined by G(ℝ) and by a sufficiently small σ‐stable arithmetic subgroup Γ of G(ℚ). Then we show that the cuspidal cohomology of Y is non trivial. Moreover we give an estimate of the growth of the cuspidal cohomology if Γ shrinks to {e} in a certain way.
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