The p-adic local monodromy theorem for fake annuli
Rendiconti del Seminario Matematico della Università di Padova, Tome 118 (2007), pp. 101-146.
@article{RSMUP_2007__118__101_0,
     author = {Kedlaya, Kiran S.},
     title = {The $p$-adic local monodromy theorem for fake annuli},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {101--146},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {118},
     year = {2007},
     mrnumber = {2378392},
     zbl = {1164.14004},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2007__118__101_0/}
}
TY  - JOUR
AU  - Kedlaya, Kiran S.
TI  - The $p$-adic local monodromy theorem for fake annuli
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2007
SP  - 101
EP  - 146
VL  - 118
PB  - Seminario Matematico of the University of Padua
UR  - http://archive.numdam.org/item/RSMUP_2007__118__101_0/
LA  - en
ID  - RSMUP_2007__118__101_0
ER  - 
%0 Journal Article
%A Kedlaya, Kiran S.
%T The $p$-adic local monodromy theorem for fake annuli
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2007
%P 101-146
%V 118
%I Seminario Matematico of the University of Padua
%U http://archive.numdam.org/item/RSMUP_2007__118__101_0/
%G en
%F RSMUP_2007__118__101_0
Kedlaya, Kiran S. The $p$-adic local monodromy theorem for fake annuli. Rendiconti del Seminario Matematico della Università di Padova, Tome 118 (2007), pp. 101-146. http://archive.numdam.org/item/RSMUP_2007__118__101_0/

[1] Y. André, Filtrations de type Hasse-Arf et monodromie p-adique, Invent. Math., 148 (2002), pp. 285-317. | MR | Zbl

[2] G. Christol, About a Tsuzuki theorem, in p-adic functional analysis (Ioannina, 2000), Lecture Notes in Pure and Appl. Math. 222, Dekker, New York, 2001, pp. 63-74. | MR | Zbl

[3] G. Christol - Z. Mebkhout, Sur le théorème de l'indice des équations différentielles p-adiques. IV, Invent. Math., 143 (2001), pp. 629-672. | MR | Zbl

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

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

[6] C. Favre - M. Jonsson, The valuative tree, Lecture Notes in Math. 1853, Springer-Verlag, Berlin, 2004. | MR | Zbl

[7] J.-M. Fontaine, Représentations p-adiques des corps locaux. I, in The Grothendieck Festschrift, Vol. II, Progr. Math. 87, Birkhäuser, Boston, pp. 249-309. | MR | Zbl

[8] R.L. Graham - D.E. Knuth - O. Patashnik, Concrete mathematics: a foundation for computer science, Addison-Wesley, Reading, MA, 1994. | MR | Zbl

[9] N.M. Katz, Une formule de congruence pour la fonction z, Exposé XXII in P. Deligne and N.M. Katz, Seminaire de Géométrie Algébrique du Bois-Marie 1967-1969: Groupes de monodromie en géométrie algébrique (SGA 7 II), Lecture Notes in Math. 340, Springer-Verlag, Berlin, 1973. | MR | Zbl

[10] K.S. Kedlaya, Descent theorems for overconvergent F-crystals, Ph.D. thesis, Massachusetts Institute of Technology, 2000, available at http://math.mit.edu/~kedlaya.

[11] K.S. Kedlaya, A p-adic local monodromy theorem, Annals of Math., 160 (2004), pp. 93-184. | MR | Zbl

[12] K.S. Kedlaya, Full faithfulness for overconvergent F-isocrystals, in Geometric aspects of Dwork theory, de Gruyter, Berlin, 2004, pp. 819-835. | MR | Zbl

[13] K.S. Kedlaya, Local monodromy for p-adic differential equations: an overview, Intl. J. of Number Theory, 1 (2005), pp. 109-154. | MR | Zbl

[14] K.S. Kedlaya, Slope filtrations revisited, Doc. Math., 10 (2005), pp. 447-525. | MR | Zbl

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

[16] K.S. Kedlaya, Semistable reduction for overconvergent F-isocrystals, I: Unipotence and logarithmic extensions, arXiv preprint math.NT/0405069 (version of 20 Jan 2007); to appear in Compos. Math. | MR | Zbl

[17] K.S. Kedlaya, Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach, arXiv preprint math.NT/0508191 (version of 2 Sep 2007); to appear in Compos. Math.. | MR | Zbl

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

[19] S. Matsuda, Katz correspondence for quasi-unipotent overconvergent isocrystals, Compos. Math., 134 (2002), pp. 1-34. | MR | Zbl

[20] S. Matsuda, Conjecture on Abbes-Saito filtration and Christol-Mebkhout filtration, in Geometric aspects of Dwork theory, de Gruyter, Berlin, 2004, pp. 845-856. | MR | Zbl

[21] Z. Mebkhout, Analogue p-adique du théorème de Turrittin et le théorème de la monodromie p-adique, Invent. Math., 148 (2002), pp. 319-351. | MR | Zbl

[22] P. Ribenboim, Théorie des valuations, second edition, Les Presses de l'Université de Montréal, Montréal, 1968. | MR | Zbl

[23] A. Shiho, Crystalline fundamental groups. II. Log convergent cohomology and rigid cohomology, J. Math. Sci. Univ. Tokyo, 9 (2002), pp. 1-163. | MR | Zbl

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

[25] N. Tsuzuki, Slope filtration of quasi-unipotent overconvergent F-isocrystals, Ann. Inst. Fourier (Grenoble) 48 (1998), pp. 379-412. | Numdam | MR | Zbl

[26] M. Vaquié, Valuations, in Resolution of singularities (Obergurgl, 1997), Progr. Math., 181, Birkhäuser, Basel, pp. 539-590. | MR | Zbl