The Riemann-Hilbert correspondence for unit $F$-crystals

The Riemann-Hilbert correspondence for unit

F

-crystals

Emerton, Matthew ; Kisin, Mark

Astérisque, no. 293 (2004) , 268 p.

MR Zbl | 1 citation dans Numdam

@book{AST_2004__293__1_0,
     author = {Emerton, Matthew and Kisin, Mark},
     title = {The {Riemann-Hilbert} correspondence for unit $F$-crystals},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {293},
     year = {2004},
     mrnumber = {2071510},
     zbl = {1056.14025},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2004__293__1_0/}
}

TY  - BOOK
AU  - Emerton, Matthew
AU  - Kisin, Mark
TI  - The Riemann-Hilbert correspondence for unit $F$-crystals
T3  - Astérisque
PY  - 2004
IS  - 293
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2004__293__1_0/
LA  - en
ID  - AST_2004__293__1_0
ER  -

%0 Book
%A Emerton, Matthew
%A Kisin, Mark
%T The Riemann-Hilbert correspondence for unit $F$-crystals
%S Astérisque
%D 2004
%N 293
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2004__293__1_0/
%G en
%F AST_2004__293__1_0

Emerton, Matthew; Kisin, Mark. The Riemann-Hilbert correspondence for unit $F$-crystals. Astérisque, no. 293 (2004), 268 p. http://numdam.org/item/AST_2004__293__1_0/

Bibliographie
Cité par

[Be] A. Beilinson - On the derived category of perverse sheaves, in $K$ -theory, arithmetic and geometry (Moscow, 1984-86), Lect. Notes in Math., vol. 1289, Springer, 1987, p. 27-41. | MR | Zbl

[BBD] A. A. Beilinson, J. N. Bernstein & P. Deligne - Faisceaux pervers, in Analyse et topologie sur les espaces singuliers (Luminy, 1981), Astérisque, vol. 100, Société Mathématique de France, Paris, 1982, p. 5-171. | MR | Zbl | Numdam

[Ber1] P. Berthelot - $𝒟$ -modules arithmétiques I. Opérateurs différentiels de niveau fini, Ann. scient. Ec. Norm. Sup. 4e série 29 (1996), p. 185-272. | MR | Zbl | EuDML | Numdam

[Ber2] P. Berthelot - $𝒟$ -modules arithmétiques II. Descente par Frobenius, Mém. Soc. math. France (N.S.), vol. 81, Société Mathématique de France, Paris, 2000. | MR | Zbl | EuDML | Numdam

[Ber3] P. Berthelot - Introduction à la théorie arithmétique des $𝒟$ -modules, in Cohomologies $p$ -adiques et applications arithmétiques (II), Astérisque, vol. 279, Société Mathématique de France, Paris, 2002, p. 1-80. | Zbl | Numdam

[Ber4] P. Berthelot - $𝒟$ -modules arithmétiques III. Images directes et inverses, in preparation.

[BP] G. Böckle & R. Pink - Cohomological Theory of Crystals over Function Fields, work in progress. | Zbl

[Bo] A. Borel (ed.) - Algebraic $𝒟$ -modules, Perspectives in Math., vol. 2, Boston, Academic Press, 1987. | Zbl

[Con] B. Conrad - Grothendieck duality and base change, Lect. Notes in Math., vol. 1750, Springer, 2000. | Zbl

[Cr] R. Crew - $L$ -functions of $p$ -adic characters and geometric Iwasawa theory, Invent. Math. 88 (1987), p. 395-403. | Zbl | EuDML | DOI

[De] P. Deligne (ed.) - Séminaire de Géométrie Algébrique du Bois-Marie SGA 4 1/2, vol. 569, Springer, 1977.

[DI] P. Deligne & L. Illusie - Relèvements modulo $p^{2}$ et décomposition du complexe de de Rham, Invent Math. 89 (1987), p. 247-270. | Zbl | EuDML | DOI

[EK1] M. Emerton & M. Kisin - An introduction to the Riemann-Hilbert correspondence for unit $F$ -crystals, to appear in the proceedings of the Dwork memorial conference. | Zbl

[EK2] M. Emerton & M. Kisin - Unit $L$ -functions and a conjecture of Katz, Ann. of Math. (2) 153 (2001), p. 329-354. | Zbl | DOI

[Fa] G. Faltings - Crystalline cohomology and $p$ -adic Galois representations, in Algebraic Analysis, Geometry, and Number Theory, Proceedings of the J AMI Inaugural Conference, The John Hopkins Univ. Press, 1989, p. 25-80. | Zbl

[Ga] O. Gabber - Notes on some $t$ -structures, to appear in the proceedings of the Dwork memorial conference. | Zbl

[SGA4] A. Grothendieck, M. Artin & J.-L. Verdier - Théorie des topos et cohomologie étale des schémas, Lect. Notes in Math., vol. 269, 270, 305, Springer, 1972-73. | Zbl

[Ha1] R. Hartshorne - Residues and Duality, Lect. Notes in Math., vol. 20, Springer, 1966. | Zbl | EuDML

[Ha2] R. Hartshorne - Algebraic Geometry, Graduate Texts in Math., vol. 52, Springer, 1977. | Zbl | DOI

[deJ] A. J. De Jong - Smoothness, semi-stability and alterations, Publ. Math. Inst. Hautes Études Sci. 83 (1996), p. 51-93. | Zbl | EuDML | Numdam | DOI

[Ka1] N. Katz - Travaux de Dwork, in Séminaire Bourbaki, Lect. Notes in Math., vol. 317, Springer, 1972, p. 167-200. | Zbl | EuDML | Numdam

[Ka2] N. Katz - $p$ -adic Properties of Modular Forms, in Modular Functions of One Variable, Lect. Notes in Math., vol. 350, Springer, 1973, p. 69-190. | Zbl | DOI

[Lyu] G. Lyubeznik - $F$ -modules: applications to local cohomology and $D$ -modules in characteristic $p > 0$ , J. reine angew. Math. 491 (1997), p. 65-130. | Zbl | EuDML

[TW] Y. Taguchi & D. Wan - $L$ -functions of $ϕ$ -sheaves and Drinfeld modules, J. Amer. Math. Soc. 9 (1996), no. 3, p. 755-781. | Zbl | DOI

[Ve] J.-L. Verdier - Base change for twisted inverse image of coherent sheaves, in International colloquium on algebraic geometry (Bombay, 1968), Oxford Univ. Press, 1969, p. 393-408. | Zbl

[Vi1] A. Virrion - Théorèmes de dualité locale et globale dans la théorie arithmétique de $𝒟$ -modules, Thèse, Université de Rennes I, 1995.

[Vi2] A. Virrion - Trace et dualité relative pour les $𝒟$ -modules arithmétiques: Complexe de Čech-Alexander et morphisme trace, prépublication IRMAR 27, 2000. | Zbl

[Wa] D. Wan - Meromorphic continuation of $L$ -functions of $p$ -adic representations, Ann. of Math. 143 (1996), p. 469-498. | Zbl | DOI

[We] C. Weibel - An introduction to homological algebra, Cambridge studies in advanced mathematics, vol. 38, Cambridge Univ. Press, 1994. | Zbl