Celebratio Mathematica — Baum — Complete Bibliography

Complete Bibliography

Works connected to Matilde Marcolli

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A.-M. Aubert, P. Baum, and R. Plymen: “The Hecke algebra of a reductive \( p \)-adic group: A geometric conjecture,” pp. 1–34 in Noncommutative geometry and number theory: Where arithmetic meets geometry and physics (Bonn, Germany, August 2003 and June 2004). Edited by C. Consani and M. Marcolli. Aspects of Mathematics 37. Vieweg (Wiesbaden, Germany), 2006. MR 2327297 Zbl 1120.14001 incollection

Let \( \mathcal{H}(G) \) be the Hecke algebra of a reductive \( p \)-adic group \( G \). We formulate a conjecture for the ideals in the Bernstein decomposition of \( \mathcal{H}(G) \). The conjecture says that each ideal is geometrically equivalent to an algebraic variety. Our conjecture is closely related to Lusztig’s conjecture on the asymptotic Hecke algebra. We prove our conjecture for \( \mathrm{SL}(2) \) and \( \mathrm{GL}(n) \). We also prove part (1) of the conjecture for the Iwahori ideals of the groups \( \mathrm{PGL}(n) \) and \( \mathrm{SO}(5) \). The conjecture, if true, leads to a parametrization of the smooth dual of \( G \) by the points in a complex affine locally algebraic variety.

Anne-Marie Aubert	Related
Roger J. Plymen	Related
Caterina Consani	Related
Matilde Marcolli	Related

P. Baum, N. Higson, and T. Schick: “A geometric description of equivariant \( K \)-homology for proper actions,” pp. 1–22 in Quanta of maths: Proceedings of meeting in honor of Alain Connes’ 60th birthday. Edited by E. Blanchard, D. Ellwood, M. Khalkhali, M. Marcolli, H. Moscovici, and S. Popa. Clay Mathematics Proceedings 11. American Mathematical Society (Providence, RI), 2010. MR 2732043 Zbl 1216.19006 ArXiv 0907.2066 incollection

Sorin Teodor Popa	Related
Étienne Blanchard	Related
Alain Connes	Related
Thomas Schick	Related
Masoud Khalkhali	Related
David Alexandre Ellwood	Related
Nigel David Higson	Related
Matilde Marcolli	Related
Henri Moscovici	Related