X. Si and . Géométriquement-connexe-et-compacte, ?, alors tous les sommets de S an (X) sont des noeuds, et ? an (X) est une triangulation de X

X. Soit and O. Et-normale-sur, Soit S(X ) l'ensemble des préimages (par la spécialisation) dans X K des points génériques des composantes irréductibles de la fibre spéciale de XX )) s'étend (de manière unique) en un automorphisme de X [28, 6.3.23]. Si X est semistable au sens large (28) , alors S(X ) est une triangulation : cela suit de ce que la préimage (par l'application de spécialisation) d'un point non singulier est un disque ouvert et celle d'un point double est une couronne ouverte. Si X est le modèle stable de l'analytification d'une courbe projective lisse X de genre ? 2, alors la triangulation S(X ) est égale à ? an (X)

M. Baker, S. Payne, and J. Rabinoff, Nonarchimedean geometry, tropicalization, and metrics on curves, Algebraic Geometry, vol.3, issue.1, pp.63-105, 2016.
DOI : 10.14231/AG-2016-004
URL : http://doi.org/10.14231/ag-2016-004

P. Bayer, On serre-duality for coherent sheaves on rigid-analytic spaces, Manuscripta Mathematica, vol.3, issue.2, pp.219-245, 1997.
DOI : 10.1007/BF02677468

J. Boutot and H. Carayol, Uniformisation p-adique des courbes de Shimura : les théorèmes de ?erednik et de Drinfel'd, Astérisque, pp.196-197, 1991.

J. Boutot and T. Zink, The p-adic uniformization of Shimura curves, preprint 2000, disponible à https

A. Caraiani, M. Emerton, T. Gee, D. Geraghty, V. Pa?k et al., Patching and the $p$-adic local Langlands correspondence, Cambridge Journal of Mathematics, vol.4, issue.2, pp.197-287, 2016.
DOI : 10.4310/CJM.2016.v4.n2.a2
URL : http://www.intlpress.com/site/pub/files/_fulltext/journals/cjm/2016/0004/0002/CJM-2016-0004-0002-a002.pdf

B. Chiarellotto, Duality in rigid analysis, in p-adic analysis (Trento, Lecture Notes in Math, pp.142-172, 1454.

R. Coleman, Reciprocity laws on curves, Compositio Math, vol.72, pp.205-235, 1989.

R. Coleman and A. Iovita, The Frobenius and monodromy operators for curves and abelian varieties, Duke Math, J, vol.97, pp.171-215, 1999.

P. Colmez, P???riodesp-adiques des vari???t???s ab???liennes, Mathematische Annalen, vol.65, issue.1, pp.629-644, 1992.
DOI : 10.1007/BF01444640

P. Colmez, Intégration sur les variétés p-adiques, Astérisque, vol.248, 1998.

P. Colmez, ESPACES DE BANACH DE DIMENSION FINIE, Journal of the Institute of Mathematics of Jussieu, vol.1, issue.03, pp.331-439, 2002.
DOI : 10.1017/S1474748002000099

P. Colmez, Espaces vectoriels de dimension finie et représentations de de Rham, Astérisque, vol.319, pp.117-186, 2008.
DOI : 10.1017/s1474748002000099

P. Colmez, Représentations de GL2(Qp) et (?, ?)-modules, Astérisque, vol.330, pp.281-509, 2010.

P. Colmez, Correspondance de Langlands locale p-adique et changement de poids, J. EMS

P. Colmez, G. Dospinescu, and W. Nizio?, Cohomology of p-adic Stein spaces, en pré- paration

P. Colmez, G. Dospinescu, V. Pa?k, and ¯. Unas, The $p$-adic local Langlands correspondence for ${\rm GL}_2(\mathbb{Q}_p)$, Cambridge Journal of Mathematics, vol.2, issue.1, pp.1-47, 2014.
DOI : 10.4310/CJM.2014.v2.n1.a1

P. Colmez and J. Fontaine, Construction des repr??sentations p-adiques semi-stables, Inventiones mathematicae, vol.140, issue.1, pp.1-43, 2000.
DOI : 10.1007/s002220000042

P. Colmez and W. Nizio?, Syntomic complexes and p-adic nearby cycles, Inventiones mathematicae, vol.103, issue.1, pp.1-108, 2017.
DOI : 10.1112/plms/pdr019
URL : https://hal.archives-ouvertes.fr/ensl-01420358

J. Dat, Th??orie de Lubin-Tate non-ab??lienne et repr??sentations elliptiques, Inventiones mathematicae, vol.13, issue.3, pp.75-152, 2007.
DOI : 10.5802/jtnb.313

G. Dospinescu, Actions infinit??simales dans la correspondance de Langlands locale p-adique, Mathematische Annalen, vol.153, issue.3, pp.627-657, 2012.
DOI : 10.1007/s00222-002-0284-1
URL : http://arxiv.org/pdf/1102.4788

G. Dospinescu and A. Bras, Revêtements du demi-plan de Drinfeld et correspondance de Langlands locale p-adique, Ann. of Math
DOI : 10.4007/annals.2017.186.2.1

V. Drinfeld, ELLIPTIC MODULES, Mathematics of the USSR-Sbornik, vol.23, issue.4, pp.594-627, 1974.
DOI : 10.1070/SM1974v023n04ABEH001731

A. Ducros, La structure des courbes analytiques, livre en préparation, version partielle disponible à https

M. Emerton, Local-global compatibility in the p-adic Langlands programme for GL 2, 2011.

G. Faltings, The trace formula and Drinfeld's upper half-plane, Duke Math, J, vol.76, pp.467-481, 1994.
DOI : 10.1215/s0012-7094-94-07616-3

G. Faltings, Almost étale extensions. Cohomologies p-adiques et applications arithmétiques, II. Astérisque No, vol.279, pp.185-270, 2002.

G. Faltings, A relation between two moduli spaces studied by V. G. Drinfeld, Contemp. Math, vol.300, pp.115-129, 2002.
DOI : 10.1090/conm/300/05145

L. Fargues and L. , isomorphisme entre les tours de Lubin-Tate et de Drinfeld et applications cohomologiques, Progr. Math, vol.262, pp.1-325, 2008.

J. Fontaine and W. , Messing, p-adic periods and p-adic étale cohomology, Current Trends in, Contemporary Math, pp.179-207, 1987.

J. M. Fontaine, Représentations -adiques potentiellement semi-stables, Astérisque, vol.223, pp.321-347, 1994.

J. Fresnel, M. Van, and . Put, Rigid analytic geometry and its applications, Progress in Mathematics, vol.218, 2004.
DOI : 10.1007/978-1-4612-0041-3

B. H. Gross and M. J. Hopkins, Equivariant vector bundles on the Lubin-Tate space, Topology and representation theory, pp.23-88, 1992.

E. Grosse-klönne, Rigid analytic spaces with overconvergent structure sheaf, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.17, issue.4, pp.73-95, 2000.
DOI : 10.1515/crll.2000.018

E. Grosse-klönne, Frobenius and monodromy operators in rigid analysis, and Drinfel'd's symmetric space, Journal of Algebraic Geometry, vol.14, issue.3, pp.391-437, 2005.
DOI : 10.1090/S1056-3911-05-00402-9

E. Grosse-klönne, De Rham cohomology of rigid spaces, Mathematische Zeitschrift, vol.247, issue.2, pp.223-240, 2004.
DOI : 10.1007/s00209-003-0544-9

M. Harris, Supercuspidal representations in the cohomology of Drinfeld's upper halfspace ; elaboration of Carayol's program, Invent. math, pp.75-119, 1997.

M. Harris and R. Taylor, The geometry and cohomology of some simple Shimura varieties , with an appendix by, Annals of Mathematics Studies, vol.151, 2001.

N. Jacobson, Structure theory of simple rings without finiteness assumptions, Transactions of the American Mathematical Society, vol.57, issue.2, pp.228-245
DOI : 10.1090/S0002-9947-1945-0011680-8

H. Jacquet and R. Langlands, Automorphic forms on GL, Lect. Notes in Math, vol.114, issue.2, 1970.
DOI : 10.1007/BFb0058988

J. De-jong, M. Van, and . Put, Étale cohomology of rigid analytic spaces, Doc. Math, vol.1, pp.1-56, 1996.

K. Kedlaya and R. Liu, Relative p-adic Hodge theory, II : Imperfect period rings
DOI : 10.1142/9789814324359_0050
URL : http://math.mit.edu/~kedlaya/papers/icm2010.pdf

Q. Liu, Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics 6, 2002.

Y. Morita, A p-adic theory of hyperfunctions, I, Publ, pp.1-24, 1981.

G. A. Mustafin, ON NON-ARCHIMEDEAN UNIFORMIZATION, Russian Mathematical Surveys, vol.33, issue.1, pp.207-237, 1978.
DOI : 10.1070/RM1978v033n01ABEH002251

J. Neková? and W. Nizio?, Syntomic cohomology and p-adic regulators for varieties over p-adic fields, Algebra & Number Theory, vol.143, issue.8, pp.1695-1790, 2016.
DOI : 10.1007/BF01587941

P. Scholze, Perfectoid Spaces, Publications math??matiques de l'IH??S, vol.20, issue.1, pp.245-313, 2012.
DOI : 10.1090/S0894-0347-06-00542-X

P. Scholze, -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES, Forum of Mathematics, Pi, vol.97, pp.1-77, 2013.
DOI : 10.1007/978-3-642-87942-5_12

P. Scholze, Perfectoid spaces: A survey, Current Developments in Mathematics, vol.2012, issue.1, 2012.
DOI : 10.4310/CDM.2012.v2012.n1.a4

P. Scholze, On the p-adic cohomology of the Lubin-Tate tower

P. Scholze and J. Weinstein, Moduli of $p$-divisible groups, Cambridge Journal of Mathematics, vol.1, issue.2, pp.145-237, 2013.
DOI : 10.4310/CJM.2013.v1.n2.a1

T. Saito, Abstract, Compositio Mathematica, vol.59, issue.1, pp.1081-1113, 2009.
DOI : 10.1215/S0012-7094-93-07211-0

P. Schneider and J. Teitelbaum, Banach space representations and Iwasawa theory, Israel Journal of Mathematics, vol.36, issue.1, pp.359-380, 2002.
DOI : 10.1007/978-1-4684-0133-2
URL : http://arxiv.org/pdf/math/0005066

P. Schneider and U. Stuhler, The cohomology ofp-adic symmetric spaces, Inventiones Mathematicae, vol.101, issue.40, pp.47-122, 1991.
DOI : 10.1515/crll.1989.400.3

M. Strauch, Geometrically Connected Components of Lubin-Tate Deformation Spaces with Level Structures, Pure and Applied Mathematics Quarterly, vol.4, issue.4, pp.1215-1232, 2008.
DOI : 10.4310/PAMQ.2008.v4.n4.a10

M. Temkin, Introduction to Berkovich analytic spaces, Berkovich spaces and applications , Springer Lecture Notes in Math, pp.3-66, 2015.
DOI : 10.1007/978-3-319-11029-5_1
URL : http://arxiv.org/pdf/1010.2235

T. Tsuji, p-adic ??tale cohomology and crystalline cohomology in the semi-stable reduction case, Inventiones Mathematicae, vol.137, issue.2, pp.233-411, 1999.
DOI : 10.1007/s002220050330

M. Van and . Put, The class group of a one-dimensional affinoid space, Ann. Inst. Fourier, vol.30, pp.155-164, 1980.

M. Van and . Put, Serre duality for rigid analytic spaces, Indag. Math, vol.3, pp.219-235, 1992.

J. Weinstein, Semistable models for modular curves of arbitrary level, Inventiones mathematicae, vol.22, issue.2, pp.459-526, 2016.
DOI : 10.5802/jtnb.728

S. Wewers, Some remarks on open analytic curves over non-archimedian fields, arXiv :math, p.509434