P. Achinger, -neighborhoods and comparison theorems, Compositio Mathematica, vol.11, issue.10, pp.1945-1964, 2015.
DOI : 10.1090/S1056-3911-2010-00555-3

F. Andreatta, Generalized ring of norms and generalized (?, ?)-modules, Ann. ENS, vol.39, pp.599-647, 2006.

F. Andreatta and O. Brinon, Surconvergence des représentations p-adiques: le cas relatif, Astérisque, vol.319, pp.39-116, 2008.

F. Andreatta and A. Iovita, Global applications of relative (?, ?)-modules I, Astérisque 319, pp.339-420, 2008.

M. Asakura and K. Sato, Syntomic cohomology and Beilinson???s Tate conjecture for $K_2$, Journal of Algebraic Geometry, vol.22, issue.3, pp.481-547, 2013.
DOI : 10.1090/S1056-3911-2012-00591-8

A. Beilinson, On the crystalline period map, Cambridge Journal of Mathematics, vol.1, issue.1, pp.1-51, 2013.
DOI : 10.4310/CJM.2013.v1.n1.a1

L. Berger, Repr??sentations p -adiques et ??quations diff??rentielles, Inventiones Mathematicae, vol.148, issue.2, pp.219-284, 2002.
DOI : 10.1007/s002220100202

B. Bhatt, M. Morrow, and P. Scholze, Integral p-adic Hodge Theory

S. Bloch, H. Esnault, and M. , p-adic deformation of algebraic cycle classes, Inventiones mathematicae, vol.34, issue.4, pp.673-722, 2014.
DOI : 10.1007/s00222-013-0461-4
URL : http://arxiv.org/abs/1203.2776

S. Bloch and K. Kato, p-Adic etale cohomology, Publications math??matiques de l'IH??S, vol.8, issue.1, pp.107-152, 1986.
DOI : 10.1007/BF02831624

S. Bloch and K. Kato, L-functions and Tamagawa numbers of motives. The Grothendieck Festschrift, Progr. Math, vol.86, pp.333-400, 1990.
DOI : 10.1007/978-0-8176-4574-8_9

O. Brinon, Repr??sentations p-adiques cristallines et de de Rham dans le cas relatif, Mémoires de la Société mathématique de France, vol.1, 2008.
DOI : 10.24033/msmf.424

X. Caruso, Représentations galoisiennes p-adiques et (?, ? )-modules, Duke Math, J, vol.162, pp.2525-2607, 2013.
DOI : 10.1215/00127094-2371976

F. Cherbonnier and P. Colmez, Repr??sentations p -adiques surconvergentes, Inventiones Mathematicae, vol.133, issue.3, pp.581-611, 1998.
DOI : 10.1007/s002220050255

P. Colmez, Theorie d'Iwasawa des Representations de de Rham d'un Corps Local, The Annals of Mathematics, vol.148, issue.2, pp.485-571, 1998.
DOI : 10.2307/121003

P. Colmez, Les conjectures de monodromie p-adique, pp.53-101, 2003.

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

J. De-jong and M. , van der Put, ´ Etale cohomology of rigid analytic spaces, Doc. Math, vol.1, pp.1-56, 1996.

P. Deligne and L. Illusie, Rel???vements modulop 2 et d???composition du complexe de de Rham, Inventiones Mathematicae, vol.64, issue.2, pp.247-270, 1987.
DOI : 10.1007/BF01389078

R. Elkik, Solutions d'´ equationsàequations`equationsà coefficients dans un anneau hensélien, Ann. ENS, vol.6, pp.553-603, 1973.

V. Ertl and W. , Nizio l, Syntomic cohomology and p-adic motivic cohomology

G. Faltings, Hodge theory, J. AMS, vol.1, pp.255-299, 1988.

G. Faltings, Crystalline cohomology and p-adic Galois representations, Algebraic analysis, geometry and number theory, pp.25-80, 1989.

G. Faltings, AlmostétaleAlmostétale extensions, Astérisque, vol.279, pp.185-270, 2002.

O. Gabber, Affine analog of the proper base change theorem, Israel Journal of Mathematics, vol.6, issue.1-3, pp.325-335, 1994.
DOI : 10.1007/BF02773001

T. Geisser, Motivic cohomology over Dedekind rings, Mathematische Zeitschrift, vol.7, issue.4, pp.773-794, 2004.
DOI : 10.1007/s00209-004-0680-x
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.170.4191

L. Herr, Sur la cohomologie galoisienne des corps $p$-adiques, Bulletin de la Société mathématique de France, vol.126, issue.4, pp.563-600, 1998.
DOI : 10.24033/bsmf.2337
URL : http://archive.numdam.org/article/BSMF_1998__126_4_563_0.pdf

A. Huber, G. Kings, and N. Naumann, Abstract, Compositio Mathematica, vol.26, issue.01, pp.235-262, 2011.
DOI : 10.1112/S0010437X10004884

O. Hyodo, A note on p-adicétaleadicétale cohomology in the semi-stable reduction case, Invent. math, pp.91-543, 1988.

K. Kato, On p-adic vanishing cycles (application of ideas of Fontaine-Messing), Algebraic Geometry, Adv. Stud. Pure Math, vol.10, pp.207-251, 1985.

K. Kato, Semistable reduction and p-adicétaleadicétale cohomology, Astérisque, vol.223, pp.269-293, 1994.

K. Kedlaya and R. Liu, Relative p-adic Hodge theory, II: Imperfect period rings
DOI : 10.1142/9789814324359_0050
URL : http://arxiv.org/abs/1004.0742

M. Kisin, Crystalline representations and F-crystals, Progr. Math, vol.253, pp.459-496, 2006.
DOI : 10.1007/978-0-8176-4532-8_7

M. Kurihara, A note on p-adicétaleadicétale cohomology, Proc. Japan Acad, pp.275-278, 1987.
DOI : 10.3792/pjaa.63.275

M. Kurihara, Abelian extensions of an absolutely unramified local field with general residue field, Inventiones Mathematicae, vol.63, issue.2, pp.451-480, 1988.
DOI : 10.1007/BF01394341

M. Lazard, Groupes analytiques p-adiques, Publ. IHES, vol.26, pp.389-603, 1965.

W. Lütkebohmert, Riemann's existence problem for ap-adic field, Inventiones Mathematicae, vol.12, issue.1, pp.309-330, 1993.
DOI : 10.1007/BF01231290

K. Morita, Galois cohomology of a p-adic field via (?, ?)-modules in the imperfect residue field case, J. Math. Sci. Univ. Tokyo, vol.15, pp.219-241, 2008.

C. Nakayama, Nearby cycles for log smooth families, Compositio Mathematica, vol.112, issue.1, pp.45-75, 1998.
DOI : 10.1023/A:1000327225021

J. Neková? and W. , Nizio l, Syntomic cohomology and p-adic regulators for varieties over p-adic fields, arXiv: 1309

S. Saito and K. Sato, -adic fields, Annals of Mathematics, vol.172, issue.3, pp.1593-1639, 2010.
DOI : 10.4007/annals.2010.172.1593
URL : https://hal.archives-ouvertes.fr/hal-00309627

T. Saito, Log smooth extension of a family of curves and semi-stable reduction, Journal of Algebraic Geometry, vol.13, issue.2, pp.287-321, 2004.
DOI : 10.1090/S1056-3911-03-00338-2

P. Scholze, Perfectoid Spaces, Publications math??matiques de l'IH??S, vol.20, issue.1, pp.245-313, 2012.
DOI : 10.1007/s10240-012-0042-x

P. Scholze, -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES, Forum of Mathematics, Pi, vol.97, pp.1-77, 2013.
DOI : 10.1017/S1474748012000643
URL : https://hal.archives-ouvertes.fr/hal-01334131

M. Somekawa, Log-Syntomic Regulators and p-Adic Polylogarithms, K-Theory, vol.17, issue.3, pp.265-294, 1999.
DOI : 10.1023/A:1007755726476

G. Tamme, On an analytic version of Lazard???s isomorphism, Algebra & Number Theory, vol.9, issue.4, pp.937-956, 2015.
DOI : 10.2140/ant.2015.9.937

F. and T. Ribeiro, Une formule explicite pour le symbole de Hilbert d???un groupe formel, Annales de l???institut Fourier, vol.61, issue.1, pp.261-318, 2011.
DOI : 10.5802/aif.2602

R. Thomason, Algebraic K-theory andétaleandétale cohomology, Ann. ENS, vol.18, pp.437-552, 1985.
DOI : 10.24033/asens.1495

T. Tsuji, Syntomic complexes and p-adic vanishing cycles, J. reine angew, Math, vol.472, pp.69-138, 1996.

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

T. Tsuji, On the $p$ adic nearby cycles of log smooth families, Bulletin de la Société mathématique de France, vol.128, issue.4, pp.529-575, 2000.
DOI : 10.24033/bsmf.2381

T. Tsuji, On the maximal unramified quotients of p-adicétaleadicétale cohomology groups and logarithmic Hodge-Witt sheaves. Kazuya Kato's fiftieth birthday, Doc. Math, pp.833-890, 2003.

A. Tyc, Differential basis, p-basis, and smoothness in characteristic p > 0, Proc. AMS, vol.103, pp.389-394, 1988.
DOI : 10.2307/2047146

S. Zerbes, Bloch-Kato exponential maps for local fields with imperfect residue fields, Proc. London Math. Soc. 103, pp.1007-1048, 2011.
DOI : 10.1112/plms/pdr019

G. Yamashita and S. Yasuda, cohomology and crystalline cohomology for the open varieties with semistable reduction, preprint, pp.p-adicétaleadicétale, 2014.

C. , I. , U. Pierre, and M. Curie, 75005 Paris, France E-mail address: pierre.colmez@imj-prg.fr CNRS