Berkovich $p$-adic analytic spaces

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1. [1] Y. André – “On a geometric description of $\mathrm{Gal}({\overline{𝐐}}_p/{𝐐}_p)$ and a $p$-adic avatar of $\widehat{GT}$”, Duke Math. J. 119 (2003), no. 1, p. 1–39. Zbl1155.11356MR1991645
2. [2] M. Baker & R. Rumely – “Analysis and dynamics on the Berkovich projective line”, prépublication. 
3. [3] —, “Equidistribution of small points, rational dynamics, and potential theory”, prépublication. Zbl1234.11082
4. [4] —, “Harmonic Analysis on Metrized graphs”, prépublication. 
5. [5] V. G. Berkovich – “Integration of one-forms on $p$-adic analytic spaces”, prépublication. Zbl1161.14001MR2263704
6. [6] —, Spectral theory and analytic geometry over non-Archimedean fields, Mathematical Surveys and Monographs, vol. 33, Amer. Math. Soc., Providence, 1990. Zbl0715.14013MR1070709
7. [7] —, “Étale cohomology for non-Archimedean analytic spaces”, Inst. Hautes Études Sci. Publ. Math.78 (1993), p. 5–161. Zbl0804.32019MR1259429
8. [8] —, “Vanishing cycles for formal schemes”, Invent. Math. 115 (1994), no. 3, p. 539–571. Zbl0791.14008MR1262943
9. [9] —, “On the comparison theorem for étale cohomology of non-Archimedean analytic spaces”, Israel J. Math. 92 (1995), no. 1-3, p. 45–59. Zbl0864.14011MR1357745
10. [10] —, “Vanishing cycles for formal schemes. II”, Invent. Math. 125 (1996), no. 2, p. 367–390. Zbl0852.14002MR1395723
11. [11] —, “Vanishing cycles for non-Archimedean analytic spaces”, J. Amer. Math. Soc. 9 (1996), no. 4, p. 1187–1209. Zbl0988.14004MR1376692
12. [12] —, “$p$-adic analytic spaces”, in Proceedings of the International Congress of Mathematicians (Berlin 1998), vol. II (extra vol.), 1998, p. 141–151 (electronic). Zbl0894.00032MR1648064
13. [13] —, “Smooth $p$-adic analytic spaces are locally contractible I”, Invent. Math. 137 (1999), no. 1, p. 1–84. Zbl0930.32016MR1702143
14. [14] —, “Smooth $p$-adic analytic spaces are locally contractible II”, in Geometric aspects of Dwork theory, Walter de Gruyter GmbH & Co. KG, Berlin, 2004, p. 293–370 (vols. I, II). Zbl1060.32010
15. [15] S. Bloch, H. Gillet & C. Soulé – “Non-Archimedean Arakelov theory”, J. Algebraic Geom. 4 (1995), no. 3, p. 427–485. Zbl0866.14011MR1325788
16. [16] S. Bosch, U. Güntzer & R. Remmert – Non-Archimedean analysis. A systematic approach to rigid analytic geometry, Grundlehren der Mathematischen Wissenschaften, vol. 261, Springer-Verlag, Berlin, 1984. Zbl0539.14017MR746961
17. [17] S. Bosch & W. Lütkebohmert – “Stable reduction and uniformization of abelian varieties. II”, Invent. Math. 78 (1984), no. 2, p. 257–297. Zbl0554.14015MR767194
18. [18] —, “Stable reduction and uniformization of abelian varieties. I”, Math. Ann. 270 (1985), no. 3, p. 349–379. Zbl0554.14012MR774362
19. [19] —, “Formal and rigid geometry I. Rigid spaces”, Math. Ann. 295 (1993), no. 2, p. 291–317. Zbl0808.14017MR1202394
20. [20] —, “Formal and rigid geometry II. Flattening techniques”, Math. Ann. 296 (1993), no. 3, p. 403–429. Zbl0808.14018MR1225983
21. [21] S. Bosch, W. Lütkebohmert & M. Raynaud – “Formal and rigid geometry III. The relative maximum principle”, Math. Ann. 302 (1995), no. 1, p. 1–29. Zbl0839.14013MR1329445
22. [22] —, “Formal and rigid geometry IV. The reduced fibre theorem”, Invent. Math. 119 (1995), no. 2, p. 361–398. Zbl0839.14014MR1312505
23. [23] P. Boyer – “Mauvaise réduction des variétés de Drinfeld et correspondance de Langlands locale”, Invent. Math. 138 (1999), no. 3, p. 573–629. Zbl1161.11408MR1719811
24. [24] H. Carayol – “Nonabelian Lubin-Tate theory”, in Automorphic forms, Shimura varieties, and $L$-functions (Ann Arbor 1988), Perspect. Math., vol. 11, Academic Press, Boston, MA, 1990, p. 15–39 (vol. II). Zbl0704.11049MR1044827
25. [25] A. Chambert-Loir – “Mesures et équidistribution sur les espaces de Berkovich”, J. reine angew. Math. 595 (2006), p. 215–235. Zbl1112.14022MR2244803
26. [26] W. Cherry – “Non-Archimedean big Picard theorems”, prépublication sur ArXiv, math.AG/0207081. MR2882389
27. [27] —, “Non-Archimedean analytic curves in abelian varieties”, Math. Ann. 300 (1994), no. 3, p. 393–404. Zbl0808.14019MR1304429
28. [28] —, “A survey of Nevanlinna theory over non-Archimedean fields”, Bull. Hong Kong Math. Soc. 1 (1997), no. 2, p. 235–249. Zbl0946.30030MR1605198
29. [29] W. Cherry & M. Ru – “Rigid analytic Picard theorems”, Amer. J. Math. 126 (2004), no. 4, p. 873–889. Zbl1055.32013MR2075485
30. [30] B. Chiarellotto – “Espaces de Berkovich et équations différentielles $p$-adiques. Une note”, Rend. Sem. Mat. Univ. Padova103 (2000), p. 193–209. Zbl0974.12014MR1789539
31. [31] R. F. Coleman – “Dilogarithms, regulators and $p$-adic $L$-functions”, Invent. Math. 69 (1982), no. 2, p. 171–208. Zbl0516.12017MR674400
32. [32] J.-L. Colliot-Thélène & R. Parimala – “Real components of algebraic varieties and étale cohomology”, Invent. Math. 101 (1990), no. 1, p. 81–99. Zbl0726.14013MR1055712
33. [33] A. Ducros – “Triangulations et cohomologie étale sur une courbe analytique”, article actuellement soumis. Zbl1163.14018
34. [34] —, “Cohomologie non ramifiée sur une courbe $p$-adique lisse”, Compositio Math. 130 (2002), no. 1, p. 89–117. Zbl1057.14021MR1883693
35. [35] —, “Image réciproque du squelette par un morphisme entre espaces de Berkovich de même dimension”, Bull. Soc. Math. France 131 (2003), no. 4, p. 483–506. Zbl1068.14024MR2044492
36. [36] —, “Parties semi-algébriques d’une variété algébrique $p$-adique”, Manuscripta Math. 111 (2003), no. 4, p. 513–528. Zbl1020.14017MR2002825
37. [37] A. Escassut & N. Mai Netti – “Shilov boundary for normed algebras”, in Topics in analysis and its applications, NATO Sci. Ser. II Math. Phys. Chem., vol. 147, Kluwer Acad. Publ., Dordrecht, 2004, p. 1–10. Zbl1085.46051MR2157105
38. [38] C. Favre & M. Jonsson – The valuative tree, Lect. Notes in Mathematics, vol. 1853, Springer-Verlag, Berlin, 2004. Zbl1064.14024MR2097722
39. [39] —, “Valuative analysis of planar plurisubharmonic functions”, Invent. Math. 162 (2005), no. 2, p. 271–311. Zbl1089.32032MR2199007
40. [40] C. Favre & J. Rivera-Letelier – “Théorème d’équidistribution de Brolin en dynamique $p$-adique”, C. R. Math. Acad. Sci. Paris 339 (2004), no. 4, p. 271–276. Zbl1052.37039MR2092012
41. [41] —, “Équidistribution quantitative des points de petite hauteur sur la droite projective”, Math. Ann. 335 (2006), no. 2, p. 311–361. Zbl1175.11029MR2221116
42. [42] H. Gillet & C. Soulé – “Direct images in non-Archimedean Arakelov theory”, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 2, p. 363–399. Zbl0969.14015MR1775354
43. [43] W. Gubler – “Local heights of subvarieties over non-Archimedean fields”, J. reine angew. Math. 498 (1998), p. 61–113. Zbl0906.14013MR1629925
44. [44] B. Guennebaud – “Sur une notion de spectre pour les algèbres normées ultramétriques”, Thèse, Université de Poitiers, 1973. 
45. [45] M. Harris – “Supercuspidal representations in the cohomology of Drinfeld upper half spaces ; elaboration of Carayol’s program”, Invent. Math.129 (1997), p. 75–119. Zbl0886.11029MR1464867
46. [46] M. Harris & R. Taylor – The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, Princeton, NJ, 2001, avec un appendice de V.G. Berkovich. Zbl1036.11027MR1876802
47. [47] T. Hausberger – “Uniformisation des variétés de Laumon-Rapoport-Stuhler et conjecture de Drinfeld-Carayol”, Ann. Inst. Fourier (Grenoble) 55 (2005), no. 4, p. 1285–1371. Zbl1138.11329MR2157169
48. [48] R. Huber – Étale cohomology of rigid analytic varieties and adic spaces, Aspects of Mathematics, E30, Friedr. Vieweg & Sohn, Braunschweig, 1996. Zbl0868.14010MR1734903
49. [49] I. Itenberg – “Amibes de variétés algébriques et dénombrement de courbes (d’après G. Mikhalkin)”, in Séminaire Bourbaki (2003/2004), Astérisque, vol. 294, Soc. Math. France, Paris, 2004, p. 335–361. Zbl1059.14067MR2111649
50. [50] A. J. de Jong – “Étale fundamental groups of non-Archimedean analytic spaces”, Compositio Math. 97 (1995), no. 1-2, p. 89–118, Special issue in honour of Frans Oort. Zbl0864.14012MR1355119
51. [51] —, “Families of curves and alterations”, Ann. Inst. Fourier (Grenoble) 47 (1997), no. 2, p. 599–621. Zbl0868.14012MR1450427
52. [52] K. Kato – “A Hasse principle for two-dimensional global fields”, J. reine angew. Math. 366 (1986), p. 142–183, avec un appendice de Jean-Louis Colliot-Thélène. Zbl0576.12012MR833016
53. [53] M. Kontsevich & Y. Soibelman – “Affine structures and non-Archimedean analytic spaces”, in The unity of mathematics, Progr. Math., vol. 244, Birkhäuser, Boston, 2006, p. 321–385. Zbl1114.14027MR2181810
54. [54] N. Maïnetti – “Sequential compactness of some analytic spaces”, J. Anal.8 (2000), p. 39–54. Zbl0987.46052MR1806394
55. [55] —, “Metrizability of some analytic affine spaces”, in $p$-adic functional analysis (Ioannina, 2000), Lect. Notes in Pure and Appl. Math., vol. 222, Dekker, New York, 2001, p. 219–225. Zbl0994.46025MR1838293
56. [56] M. Raynaud – “Géométrie analytique rigide d’après Tate, Kiehl, ...”, in Table Ronde d’Analyse non archimédienne (Paris 1972), Mém. Soc. Math. France, vol. 39–40, Soc. Math. France, Paris, 1974, p. 319–327. Zbl0299.14003MR470254
57. [57] J. Rivera-Letelier – “Théorie de Julia et Fatou sur la droite hyperbolique $p$-adique”, en préparation. 
58. [58] —, “Dynamique des fonctions rationnelles sur des corps locaux”, in Geometric methods in dynamics II, Astérisque, vol. 287, Soc. Math. France, Paris, 2003, p. 147–230. Zbl1140.37336MR2040006
59. [59] —, “Espace hyperbolique $p$-adique et dynamique des fonctions rationnelles”, Compositio Math. 138 (2003), no. 2, p. 199–231. Zbl1041.37021MR2018827
60. [60] —, “Points périodiques des fonctions rationnelles dans l’espace hyperbolique $p$-adique”, Comment. Math. Helv. 80 (2005), no. 3, p. 593–629. Zbl1140.37337MR2165204
61. [61] L. Szpiro, E. Ullmo & S. Zhang – “Équirépartition des petits points”, Invent. Math. 127 (1997), no. 2, p. 337–347. Zbl0991.11035MR1427622
62. [62] J. Tate – “Rigid analytic spaces”, Invent. Math.12 (1971), p. 257–289. Zbl0212.25601MR306196
63. [63] M. Temkin – “On local properties of non-Archimedean analytic spaces”, Math. Ann. 318 (2000), no. 3, p. 585–607. Zbl0972.32019MR1800770
64. [64] —, “On local properties of non-Archimedean analytic spaces. II”, Israel J. Math.140 (2004), p. 1–27. Zbl1066.32025MR2054837
65. [65] —, “A new proof of the Gerritzen-Grauert theorem”, Math. Ann. 333 (2005), no. 2, p. 261–269. Zbl1080.32021MR2195115
66. [66] A. Thuillier – “Théorie du potentiel sur les courbes en géométrie analytique non archimédienne. Applications à la théorie d’Arakelov”, Thèse, IRMAR, Université Rennes 1, 2005. 

1. Antoine Ducros, Les espaces de Berkovich sont excellents