Espaces symétriques 𝔭 -adiques, mesures 𝔭 -adiques et transformations intégrales

Igor Potemine

Séminaire de théorie spectrale et géométrie (1996-1997)

  • Volume: 15, page 59-84
  • ISSN: 1624-5458

How to cite

top

Potemine, Igor. "Espaces symétriques $\mathfrak {p}$-adiques, mesures $\mathfrak {p}$-adiques et transformations intégrales." Séminaire de théorie spectrale et géométrie 15 (1996-1997): 59-84. <http://eudml.org/doc/114415>.

@article{Potemine1996-1997,
author = {Potemine, Igor},
journal = {Séminaire de théorie spectrale et géométrie},
language = {fre},
pages = {59-84},
publisher = {Institut Fourier},
title = {Espaces symétriques $\mathfrak \{p\}$-adiques, mesures $\mathfrak \{p\}$-adiques et transformations intégrales},
url = {http://eudml.org/doc/114415},
volume = {15},
year = {1996-1997},
}

TY - JOUR
AU - Potemine, Igor
TI - Espaces symétriques $\mathfrak {p}$-adiques, mesures $\mathfrak {p}$-adiques et transformations intégrales
JO - Séminaire de théorie spectrale et géométrie
PY - 1996-1997
PB - Institut Fourier
VL - 15
SP - 59
EP - 84
LA - fre
UR - http://eudml.org/doc/114415
ER -

References

top
  1. [AV] Y. AMICE, J. VÉLU, Distributions p-adiques associées aux séries de Hecke, Astérisque . 24-25 ( 1975), 119-131. Zbl0332.14010MR376534
  2. [BGR] S. BOSCH, U. GÜNTZER, R. REMMERT, Non-archimedean analysis, Springer, 1984. Zbl0539.14017MR746961
  3. [BS] A. BOREL, J.-P. SERRE, Cohomologie d'immeubles et de groupes S-arithmétiques, Topology 15 ( 1976), 211-232. Zbl0338.20055MR447474
  4. [BC] J.-F. BOUTOT, H. CARAYOL, Uniformisation p-adique des courbes de Shimura : les théorèmes de Cerednik et Drinfeld, Courbes modulaires et courbes de Shimura, Astérisque 196-197 ( 1991). Zbl0781.14010MR1141456
  5. [Br] K. BROWN, Buildings, Springer, 1989. Zbl0715.20017MR969123
  6. [BT] F. BRUHAT, J. TITS, Groupes réductifs sur un corps local. I. Données radicielles valuées, Publ. Math. IHES 41 ( 1972), 5-251. Zbl0254.14017MR327923
  7. [CR] G. CRISTOL, Equations différentielles p-adiques. Application aux sommes exponentielles, d'après un manuscript de Ph. Robba, Hermann, Paris, 1994. MR1411447
  8. [DH] P. DELIGNE, D. HUSEMÖLLER, Survey of Drinfeld modules, Contemp. Math., 67 ( 1987), 25-91. Zbl0627.14026MR902591
  9. [Dr1] V.G. DRINFELD, Modules elliptiques (en russe), Mat. Sbornik, 94 ( 1974), 594-627 ; Transl. angl. : Math. USSR S., 23 ( 1974), 561-592. Zbl0321.14014MR384707
  10. [Dr1] V.G. DRINFELD, Coverings of p-adic symmetric regions, Functional Analysis and its Applications 10, 2 ( 1976), 29-40. Zbl0346.14010MR422290
  11. [FvdP] J. FRESNEL, M. VAN DER PUT, Géométrie analytique rigide et applications, Birkhaüser, 1981. Zbl0479.14015MR644799
  12. [Ge] A. GENESTIER, Espaces symétrique de Drinfeld, Astérisque 23 ( 1996). Zbl0912.14015MR1393015
  13. [GvdP] L. GERRITZEN, M. VAN DER PUT, Schottky groups and Mumford curves, Lect. Notes Math. 817, Springer, 1980. Zbl0442.14009MR590243
  14. [GI] O. GOLDMAN, N. IWAHORI, The space of p-adic norms, Acta Math. 109 ( 1963), 137-177. Zbl0133.29402MR144889
  15. [GO] D. GOSS, The algebraist's upper half-plane, Bull. Amer. Math. Soc., 2, n° 3 ( 1980), 391-415. Zbl0433.14017MR561525
  16. [He] S. HELGASON, Differential geometry, Lie groups and symmetric spaces, Academic Press, 1978. Zbl0451.53038MR514561
  17. [Ko1] N. KOBLITZ, p-adic numbers, p-adic analysis and zeta-functions, Springer, 1977. Zbl0364.12015MR466081
  18. [Ko2] N. KOBLITZ, p-adic analysis: a short course on recent work, Cambridge Univ. Press, 1980. Zbl0439.12011MR591682
  19. [La] E. LANDVOGT, Compactification of Bruhat-Tits building, Lect. Notes Math. 1619, Springer, 1995. Zbl0935.20034
  20. [Ma] YU.I. MANIN, Périodes des formes paraboliques et séries de Hecke p-adiques (en russe), Mat. Sbornik 92 ( 1973), n° 3, 378-401. Zbl0293.14007
  21. [MSD] B. MAZUR, H.P.F. SWINNERTON-DYER, Arithmetic of Weil curves, Invent. Math. 25 ( 1974), No. 1, 1-35. Zbl0281.14016MR354674
  22. [MTT] B. MAZUR, J. TATE AND J. TEITELBAUM, On p-adic analogues of the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 84 ( 1986), 1-48. Zbl0699.14028MR830037
  23. [Mum] D. MUMFORD, Analytic construction of degenerating curves over complete local fields, Compositio Math. 24 ( 1972), 129-174. Zbl0228.14011MR352105
  24. [Mus] G.A. MUSTAFIN, Nonarchimedean uniformization, Math. USSR Sb. 34 ( 1978), 187-214. Zbl0411.14006
  25. [Pa] A.A. PANCHISHKIN, Non-archimedean L-functions of Siegel and Hilbert modular forms, Lect. Notes Math. 1471,Springer, 1991. Zbl0732.11026MR1122593
  26. [Re] M. REVERSAT, Lecture on rigid geometry, Arithmetic of Function Fields, D. Goss, D. Hayes and M. Rosen (eds.), W. de Gruyter, 1992, 189-207. Zbl0794.14008MR1196517
  27. [Ro] M. RONAN, Lectures on Buildings, Perspectives in Math. 7, Academic Press, 1989. Zbl0694.51001MR1005533
  28. [Sch] P. SCHNEIDER, Rigid analytic L-transforms, Lect. Notes Math. 1068,Springer ( 1983), 216-230. Zbl0572.14014MR756097
  29. [SS] P. SCHNEIDER, U. STUHLER, The cohomology of p-adic symmetric spaces, Invent. Math. 105 ( 1991), 47-122. Zbl0751.14016MR1109620
  30. [ST] P. SCHNEIDER, J. TEITELBAUM, An integral transform for p-adic symmetric spaces, Duke Math. J. Zbl0885.14012MR1432303
  31. [Se] J.-P. SERRE, Arbres, amalgames et SL(2), Astérisque 46, 1977. Zbl0369.20013
  32. [Sh] G. SHIMURA, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press, 1971. Zbl0221.10029MR314766
  33. [Ta] J. TATE, Rigid analytic spaces, Invent. Math. 12 ( 1971), 257-289. Zbl0212.25601MR306196
  34. [Te1] J. TEITELBAUM, Values of p-adic L-functions and a p-adic Poisson kernel, Invent. Math. 101 ( 1990), 395-410. Zbl0731.11065MR1062968
  35. [Te2] J. TEITELBAUM, The Poisson kernel for Drinfeld modular forms, J. Amer. Math. Soc. 4 ( 1991), 491-511. Zbl0735.11025MR1099281
  36. [Te3] J. TEITELBAUM, Rigid analytic modular forms : an integral transform approach, Arithmetic of Function Fields, D. Goss, D. Hayes and M. Rosen (eds.), W. de Gruyter, 1992, 189-207. Zbl0802.11024MR1196520
  37. [Te4] J. TEITELBAUM, The geometry of p-adic symmetric spaces, Notices of the AMS 42, No. 10 ( 1995), 1120-1126. Zbl1042.11520MR1350009
  38. [vdPV] M. VAN DER PUT, H. VOSKUIL, Symmetric spaces associated to split algebraic groups over a local field, J. reine angew. Math. 433 ( 1992), 69-100. Zbl0753.14018MR1191600
  39. [Vi] M.M. VISHIK, Mesures non archimédiennes liées aux séries de Dirichlet (en russe), Mat. Sbornik, 99 ( 1976), n° 2, 248-260 ; Math. USSR-Sb. 28 ( 1976), 216-228 (en anglais). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.