✦ LIBER ✦
On Cuspidal Cohomology of Arithmetic Groups and Cyclic Base Change
✍ Scribed by Jürgen Rohlfs; Birgit Speh
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 513 KB
- Volume
- 158
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Let F be a totally real number field and let E|F be a cyclic Galois extension with Galois group generated by σ. Let G~0~|F be a connected semi simple algebraic group defined over F, put G = res ℚ(G~0~ x ~F~E) and assume that G~0~(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.