Slope filtrations for relative Frobenius

Kedlaya, Kiran S.

Représentations

p

-adiques de groupes

p

-adiques I : représentations galoisiennes et

(φ, Γ)

-modules, Astérisque, no. 319 (2008), pp. 259-301.

MR Zbl | 3 citations dans Numdam

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     author = {Kedlaya, Kiran S.},
     title = {Slope filtrations for relative {Frobenius}},
     booktitle = {Repr\'esentations $p$-adiques de groupes $p$-adiques I : repr\'esentations galoisiennes et $(\varphi, \Gamma)$-modules},
     editor = {Berger Laurent and Breuil Christophe and Colmez Pierre},
     series = {Ast\'erisque},
     pages = {259--301},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {319},
     year = {2008},
     mrnumber = {2493220},
     zbl = {1168.11053},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2008__319__259_0/}
}

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Kedlaya, Kiran S. Slope filtrations for relative Frobenius, dans Représentations $p$-adiques de groupes $p$-adiques I : représentations galoisiennes et $(\varphi, \Gamma)$-modules, Astérisque, no. 319 (2008), pp. 259-301. http://archive.numdam.org/item/AST_2008__319__259_0/

Bibliographie
Cité par

[1] Revêtements étales et groupe fondamental (SGA 1) - Documents Mathématiques, vol. 3, Société Mathématique de France, 2003.

[2] Y. André - "Différentielles non commutatives et théorie de Galois différentielle ou aux différences", Ann. Sci. École Norm. Sup. (4) 34 (5) (2001), p. 685-739. | DOI | EuDML | Numdam | MR | Zbl

[3] J. Bellaïche & G. Chenevier - " $p$ -adic families of Galois representations and higher rank Selmer groups", preprint arXiv:math.NT/0602340, 2007. | MR

[4] L. Berger - "Représentations $p$ -adiques et équations différentielles", Invent. Math. 148 (2002), p. 219-284. | MR | Zbl

[5] L. Berger, "Équations différentielles $p$ -adiques et $(ϕ, N)$ -modules filtrés", preprint arXiv:math.NT/0406601, 2004.

[6] L. Berger & P. Colmez - "Familles de représentations de de Rham et monodromie $p$ -adique", in this volume. | Numdam | Zbl

[7] V. G. Berkovich - Spectral theory and analytic geometry over non-Archimedean fields, Mathematical Surveys and Monographs, vol. 33, American Mathematical Society, 1990. | MR | Zbl

[8] H. Cartan & S. Eilenberg - Homological algebra, Princeton University Press, 1956. | MR | Zbl

[9] F. Cherbonnier & P. Colmez - "Représentations $p$ -adiques surconvergentes", Invent. Math. 133 (1998), p. 581-611. | DOI | MR | Zbl

[10] R. Coleman & B. Mazur - "The eigencurve", in Galois representations in arithmetic algebraic geometry (Durham, 1996), London Math. Soc. Lecture Note Ser., vol. 254, Cambridge Univ. Press, 1998, p. 1-113. | MR | Zbl

[11] P. Colmez - "Les conjectures de monodromie $p$ -adiques", Astérisque 290 (2003), p. 53-101, Séminaire Bourbaki, vol. 2001/2002, exposé n° 897. | EuDML | Numdam | MR | Zbl

[12] P. Colmez, "La série principale unitaire de $G L_{2} (ℚ_{p})$ ", preprint http://www.math. jussieu. fr/~colmez/, 2007. | MR

[13] P. Colmez,"Representations triangulines de dimension $2$ ", in this volume. | Numdam | Zbl

[14] R. Crew - "Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve", Ann. Sci. École Norm. Sup. (4) 31 (1998), p. 717-763. | DOI | EuDML | Numdam | MR | Zbl

[15] P. Deligne - "La conjecture de Weil. II", Publ. Math. I.H.É.S. 52 (1980), p. 137-252. | DOI | EuDML | Numdam | MR | Zbl

[16] U. Hartl - "On a conjecture of Rapoport and Zink", preprint arXiv:math.NT/0605254, 2006. | MR | Zbl

[17] P. Colmez, "Period spaces for Hodge structures in equal characteristic", preprint arXiv:math.NT/0511686, 2006.

[18] U. Hartl & R. Pink - "Vector bundles with a Frobenius structure on the punctured unit disc", Compos. Math. 140 (2004), p. 689-716. | DOI | MR | Zbl

[19] A. J. De Jong - "Homomorphisms of Barsotti-Tate groups and crystals in positive characteristic", Invent. Math. 134 (1998), p. 301-333. | DOI | MR | Zbl

[20] K. S. Kedlaya - "Full faithfulness for overconvergent $F$ -isocrystals", in Geometric aspects of Dwork theory. Vol. I, II, Walter de Gruyter, 2004, p. 819-835. | MR | Zbl

[21] K. S. Kedlaya,"A $p$ -adic local monodromy theorem", Ann. of Math. (2) 160 (2004), p. 93-184. | DOI | MR | Zbl

[22] K. S. Kedlaya,"Slope filtrations revisited", Doc. Math. 10 (2005), p. 447-525. | EuDML | MR | Zbl

[23] K. S. Kedlaya,"Finiteness of rigid cohomology with coefficients", Duke Math. J. 134 (2006), p. 15-97. | DOI | MR | Zbl

[24] K. S. Kedlaya,"Fourier transforms and $p$ -adic 'Weil II'", Compos. Math. 142 (2006), p. 1426-1450. | DOI | MR | Zbl

[25] C. Khare & J.-P. Wintenberger - "Serre's modularity conjecture I", preprint http://www.math.utah.edu/~shekhar, 2006. | MR | Zbl

[26] C. Khare & J.-P. Wintenberger, "Serre's modularity conjecture II", preprint http://www.math.utah.edu/~shekhar, 2006. | Zbl

[27] M. Kisin - "Crystalline representations and $F$ -crystals", in Algebraic geometry and number theory, Progr. Math., vol. 253, Birkhäuser, 2006, p. 459-496. | DOI | MR | Zbl

[28] M. Kisin - "The Fontaine-Mazur conjecture for $G L_{2}$ ", preprint http://math.uchicago.edu/~kisin, 2006. | MR | Zbl

[29] M. Lazard - "Les zéros des fonctions analytiques d'une variable sur un corps value complet", Publ. Math. I.H.É.S. 14 (1962), p. 47-75. | DOI | EuDML | Numdam | MR

[30] A. H. M. Levelt - "Jordan decomposition for a class of singular differential operators", Ark. Mat. 13 (1975), p. 1-27. | DOI | MR | Zbl

[31] B. Malgrange - "Connexions méromorphes. II. Le réseau canonique", Invent. Math. 124 (1996), p. 367-387. | DOI | MR | Zbl

[32] J. I. Manin - "Theory of commutative formal groups over fields of finite characteristic", Uspehi Mat. Nauk 18 (1963), p. 3-90. | MR | Zbl

[33] V. Mehta & A. Ramanathan - "Semistable sheaves on projective varieties and their restriction to curves", Math. Ann. 258 (1981/82), p. 213-224. | DOI | EuDML | MR | Zbl

[34] M. S. Narasimhan & C. S. Seshadri - "Stable bundles and unitary bundles on a compact Riemann surface", Proc. Nat. Acad. Sci. U.S.A. 52 (1964), p. 207-211. | DOI | MR | Zbl

[35] M. S. Narasimhan & C. S. Seshadri, "Stable and unitary vector bundles on a compact Riemann surface", Ann. of Math. (2) 82 (1965), p. 540-567. | DOI | MR | Zbl

[36] O. Ore - "Theory of non-commutative polynomials", Ann. of Math. (2) 34 (1933), p. 480-508. | DOI | JFM | MR | Zbl

[37] D. S. Passman - The algebraic structure of group rings, Robert E. Krieger Publishing Co. Inc., 1985, Reprint of the 1977 original. | MR

[38] C. Praagman - "The formal classification of linear difference operators", Nederl. Akad. Wetensch. Indag. Math. 45 (1983), p. 249-261. | DOI | MR | Zbl

[39] M. Van Der Put & M. F. Singer - Galois theory of difference equations, Lecture Notes in Mathematics, vol. 1666, Springer, 1997, errata at http://www4.ncsu.edu/~singer/papers/errata.ps. | MR | Zbl

[40] M. Rapoport & T. Zink - Period spaces for $p$ -divisible groups, Annals of Mathematics Studies, vol. 141, Princeton University Press, 1996. | MR | Zbl

[41] N. Tsuzuki - "The overconvergence of morphisms of etale $ϕ - \nabla$ -spaces on a local field", Compositio Math. 103 (1996), p. 227-239. | EuDML | Numdam | MR | Zbl

[42] N. Tsuzuki, "Finite local monodromy of overconvergent unit-root $F$ -isocrystals on a curve", Amer. J. Math. 120 (1998), p. 1165-1190. | DOI | MR | Zbl