Celebratio Mathematica

Paul Baum

Contribution to Celebratio Mathematica

Works connected to Roger J. Plymen

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P. Baum, N. Hig­son, and R. Ply­men: “Equivari­ant ho­mo­logy for \( \mathrm{SL}(2) \) of a \( p \)-ad­ic field,” pp. 1–​18 in In­dex the­ory and op­er­at­or al­geb­ras (Boulder, CO, 6–10 Au­gust 1991). Edi­ted by J. Fox and P. Haskell. Con­tem­por­ary Math­em­at­ics 148. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1993. MR 1228497 Zbl 0844.​46043 incollection

P. Baum, N. Hig­son, and R. Ply­men: “A proof of the Baum–Connes con­jec­ture for \( p \)-ad­ic \( \mathrm{GL}(n) \),” C. R. Acad. Sci. Par­is Sér. I Math. 325 : 2 (July 1997), pp. 171–​176. MR 1467072 Zbl 0918.​46061 article

P. F. Baum, N. Hig­son, and R. J. Ply­men: “Rep­res­ent­a­tion the­ory of \( p \)-ad­ic groups: A view from op­er­at­or al­geb­ras,” pp. 111–​149 in The math­em­at­ic­al leg­acy of Har­ish-Chandra: A cel­eb­ra­tion of rep­res­ent­a­tion the­ory and har­mon­ic ana­lys­is (Bal­timore, MD, 9–10 Janu­ary 1998). Edi­ted by R. Dor­an and V. Varada­ra­jan. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics 68. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2000. MR 1767895 Zbl 0982.​19006 incollection

P. Baum, S. Mil­ling­ton, and R. Ply­men: “A proof of the Baum–Connes con­jec­ture for re­duct­ive ad­el­ic groups,” C. R. Acad. Sci. Par­is Sér. I Math. 332 : 3 (February 2001), pp. 195–​200. MR 1817360 Zbl 1105.​19300 article

P. Baum, S. Mil­ling­ton, and R. Ply­men: “Loc­al-glob­al prin­ciple for the Baum–Connes con­jec­ture with coef­fi­cients,” \( K \)-The­ory 28 : 1 (2003), pp. 1–​18. MR 1988816 Zbl 1034.​46073 article

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

A.-M. Au­bert, P. Baum, and R. Ply­men: “Geo­met­ric struc­ture in the rep­res­ent­a­tion the­ory of \( p \)-ad­ic groups,” C. R. Math. Acad. Sci. Par­is 345 : 10 (2007), pp. 573–​578. Part II was pub­lished in Har­mon­ic ana­lys­is on re­duct­ive, \( p \)-ad­ic groups (2011), but with “re­duct­ive” in the title. MR 2374467 Zbl 1128.​22009 article

A.-M. Au­bert, P. Baum, and R. Ply­men: “Geo­met­ric struc­ture in the prin­cip­al series of the \( p \)-ad­ic group \( \textrm{G}_2 \),” Rep­res­ent. The­ory 15 (2011), pp. 126–​169. MR 2772586 Zbl 1268.​22015 article

A.-M. Au­bert, P. Baum, and R. Ply­men: “Geo­met­ric struc­ture in the rep­res­ent­a­tion the­ory of re­duct­ive \( p \)-ad­ic groups, II,” pp. 71–​90 in Har­mon­ic ana­lys­is on re­duct­ive, \( p \)-ad­ic groups (San Fran­cisco, 16 Janu­ary 2010). Edi­ted by R. S. Dor­an, P. J. Sally, Jr., and L. Spice. Con­tem­por­ary Math­em­at­ics 543. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2011. Part I was pub­lished in C. R. Math. Acad. Sci. Par­is 345:10 (2007), doesn’t in­clude “re­duct­ive” in title. MR 2798423 Zbl 1246.​22019 incollection

A.-M. Au­bert, P. Baum, R. Ply­men, and M. Sol­leveld: “Geo­met­ric struc­ture in smooth dual and loc­al Lang­lands con­jec­ture,” Jpn. J. Math. 9 : 2 (September 2014), pp. 99–​136. Ex­pos­it­ory art­icle based on the Tak­agi lec­tures. MR 3258616 Zbl 1371.​11097 article

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

A.-M. Au­bert, P. Baum, R. Ply­men, and M. Sol­leveld: “Geo­met­ric struc­ture for the prin­cip­al series of a split re­duct­ive \( p \)-ad­ic group with con­nec­ted centre,” J. Non­com­mut. Geom. 10 : 2 (2016), pp. 663–​680. MR 3519048 Zbl 1347.​22013 article

A.-M. Au­bert, P. Baum, R. Ply­men, and M. Sol­leveld: “The loc­al Lang­lands cor­res­pond­ence for in­ner forms of \( \mathrm{SL}_n \),” Res. Math. Sci. 3 (2016). pa­per no. 32. MR 3579297 Zbl 06663301 article

A.-M. Au­bert, P. Baum, R. Ply­men, and M. Sol­leveld: “Depth and the loc­al Lang­lands cor­res­pond­ence,” pp. 17–​41 in Arbeit­sta­gung Bonn 2013: In memory of Friedrich Hirzebruch (Bonn, Ger­many, 22–28 May 2013). Edi­ted by W. Ball­mann, C. Blohmann, G. Falt­ings, P. Teich­ner, and D. Za­gi­er. Pro­gress in Math­em­at­ics 319. Birkhäuser/Spring­er In­ter­na­tion­al (Cham, Switzer­land), 2016. MR 3618046 Zbl 06748683 incollection

A.-M. Au­bert, P. Baum, R. Ply­men, and M. Sol­leveld: “Hecke al­geb­ras for in­ner forms of \( p \)-ad­ic spe­cial lin­ear groups,” J. Inst. Math. Jussieu 16 : 2 (2017), pp. 351–​419. MR 3615412 Zbl 06704330 article

A.-M. Au­bert, P. Baum, R. Ply­men, and M. Sol­leveld: “The prin­cip­al series of \( p \)-ad­ic groups with dis­con­nec­ted cen­ter,” Proc. Lond. Math. Soc. (3) 114 : 5 (2017), pp. 798–​854. MR 3653247 Zbl 06778792 article

A.-M. Au­bert, P. Baum, R. Ply­men, and M. Sol­leveld: “Con­jec­tures about \( p \)-ad­ic groups and their non­com­mut­at­ive geo­metry,” pp. 15–​51 in Around Lang­lands cor­res­pond­ences (Or­say, France, 17–20 June 2015). Edi­ted by F. Brumley, M. P. Gómez Apar­i­cio, and A. Minguez. Con­tem­por­ary Math­em­at­ics 691. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2017. MR 3666049 ArXiv 1508.​02837 incollection

A.-M. Au­bert, P. Baum, R. Ply­men, and M. Sol­leveld: “Smooth du­als of in­ner forms of \( \mathrm{ GL}_n \) and \( \mathrm{ SL}_n \),” Doc. Math. 24 (2019), pp. 373–​420. MR 3960124 article