About the difficulty to prove the Baum Connes conjecture without coefficient for a non-cocompact lattice in $Sp_4$ in a local field

Benben Liao

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arXiv · 1411.6151

About the difficulty to prove the Baum Connes conjecture without coefficient for a non-cocompact lattice in $Sp_4$ in a local field

Benben Liao

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Abstract

We introduce property $(T_{Schur},G,K)$ and prove it for some non-cocompact lattice in $Sp_4$ in a local field of finite characteristic. We show that property $(T_{Schur},G,K)$ for a non-cocompact lattice $\Gamma$ in a higher rank almost simple algebraic group in a local field is an obstacle to proving the Baum Connes conjecture without coefficient for $\Gamma$ with known methods, and this is stronger than the well-known fact that $\Gamma$ does not have the property of rapid decay (property (RD)). It is the first example (as announced in [Laf10a]) for which all known methods for proving the Baum Connes conjecture without coefficient fail.

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Benben Liao. 2014-11-22. About the difficulty to prove the Baum Connes conjecture without coefficient for a non-cocompact lattice in $Sp_4$ in a local field. https://arxiv.org/abs/1411.6151

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