Celebratio Mathematica — Baum — Complete Bibliography

Complete Bibliography

Works connected to Peter Schneider

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P. Baum and P. Schneider: “Equivariant-bivariant Chern character for profinite groups,” \( K \)-Theory 25 : 4 (2002), pp. 313–353. MR 1914452 Zbl 0997.55010 article

For the action of a locally compact and totally disconnected group \( G \) on a pair of locally compact spaces \( X \) and \( Y \) we construct, by sheaf theoretic means, a new equivariant and bivariant cohomology theory. If we take for the first space \( Y \) an universal proper \( G \)-action then we obtain for the second space its delocalized equivariant homology. This is in exact formal analogy to the definition of equivariant \( K \)-homology by Baum, Connes, Higson starting from the bivariant equivariant Kasparov \( KK \)-theory. Under certain basic finiteness conditions on the first space \( Y \) we conjecture the existence of a Chern character from the equivariant Kasparov \( KK \)-theory of \( Y \) and \( X \) into our cohomology theory made two-periodic which becomes an isomorphism upon tensoring the \( KK \) theory with the complex numbers. This conjecture is proved for profinite groups \( G \). An essential role in our construction is played by a bivariant version of Segal localization which we establish for \( KK \)-theory.

A.-M. Aubert, P. Baum, R. Plymen, and M. Solleveld: “On the local Langlands correspondence for non-tempered representations,” Münster J. Math. 7 : 1 (2014), pp. 27–50. Dedicated to Peter Schneider on the occasion of his 60th birthday. MR 3271238 Zbl 06382808 ArXiv 1303.0828 article

Let \( G \) be a reductive \( p \)-adic group. We study how a local Langlands correspondence for irreducible tempered \( G \)-representations can be extended to a local Langlands correspondence for all irreducible smooth representations of \( G \). We prove that, under a natural condition involving compatibility with unramified twists, this is possible in a canonical way.

To this end we introduce analytic \( \mathrm{R} \)-groups associated to non-tempered essentially square-integrable representations of Levi subgroups of \( G \). We establish the basic properties of these new \( \mathrm{R} \)-groups, which generalize Knapp–Stein \( \mathrm{R} \)-groups.

Anne-Marie Aubert	Related
Roger J. Plymen	Related
Peter Schneider	Related
Maarten Solleveld	Related