Crystalline cohomology of algebraic stacks and Hyodo-Kato comohology

Geodesic

Parcourir par

Olsson, Martin C.

Astérisque, no. 316 (2007) , 416 p.

Voir la notice du livre provenant de la source Numdam

MR Zbl

@book{AST_2007__316__1_0,
     author = {Olsson, Martin C.},
     title = {Crystalline cohomology of algebraic stacks and {Hyodo-Kato} comohology},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {316},
     year = {2007},
     mrnumber = {2451400},
     zbl = {1199.14006},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/AST_2007__316__1_0/}
}

TY  - BOOK
AU  - Olsson, Martin C.
TI  - Crystalline cohomology of algebraic stacks and Hyodo-Kato comohology
T3  - Astérisque
PY  - 2007
IS  - 316
PB  - Société mathématique de France
UR  - https://geodesic-test.mathdoc.fr/item/AST_2007__316__1_0/
LA  - en
ID  - AST_2007__316__1_0
ER  -

%0 Book
%A Olsson, Martin C.
%T Crystalline cohomology of algebraic stacks and Hyodo-Kato comohology
%S Astérisque
%D 2007
%N 316
%I Société mathématique de France
%U https://geodesic-test.mathdoc.fr/item/AST_2007__316__1_0/
%G en
%F AST_2007__316__1_0

Olsson, Martin C. Crystalline cohomology of algebraic stacks and Hyodo-Kato comohology. Astérisque, no. 316 (2007), 416 p. https://geodesic-test.mathdoc.fr/item/AST_2007__316__1_0/

Bibliographie
Cité par

[1] D. Abramovich, M. C. Olsson & A. Vistoli - "Tame stacks in positive characteristic", to appear in Ann. Inst Fourier (Grenoble) 58 (2008), no. 4. | MR | Zbl | EuDML | mathdoc-id | DOI

[2] D. Abramovich & A. Vistoli - "Compactifying the space of stable maps", J. Amer. Math. Soc. 15 (2002), no. 1, p. 27-75. | MR | Zbl | DOI

[3] M. Artin - "Algebraic approximation of structures over complete local rings", Publ. Math. Inst. Hautes Études Sci. 36 (1969), p. 23-58. | MR | Zbl | EuDML | mathdoc-id | DOI

[4] M. Artin, "Versal deformations and algebraic stacks", Invent. Math. 27 (1974), p. 165-189. | MR | Zbl | EuDML | DOI

[5] M. Artin, A. Grothendieck & J.-L. Verdier - Théorie des topos et cohomologie étale des schémas, Lecture Notes in Math., vol. 269, 270 & 305, Springer-Verlag, Berlin, 1972. | MR | Zbl

[6] P. Berthelot, A. Grothendieck & L. Illusie - Théorie des intersections et théorème de Riemann-Roch (SGA 6), Lecture Notes in Math., vol. 225, Springer-Verlag, Berlin, 1971. | MR | Zbl

[7] P. Berthelot - Cohomologie cristalline des schémas de caractéristique $p > 0$ , Lecture Notes in Math., vol. 407, Springer-Verlag, Berlin, 1974. | MR | Zbl

[8] P. Berthelot & A. Ogus - Notes on crystalline cohomology, Princeton University Press, Princeton, N.J., 1978. | MR | Zbl

[9] P. Berthelot & A. Ogus, " $F$ -isocrystals and de Rham cohomology. I", Invent. Math. 72 (1983), no. 2, p. 159-199. | MR | Zbl | EuDML | DOI

[10] S. Bloch - "Algebraic $K$ -theory and crystalline cohomology", Publ. Math. Inst. Hautes Études Sci. 47 (1977), p. 187-268. | MR | Zbl | EuDML | mathdoc-id | DOI

[11] B. Conrad & A. J. De Jong - "Approximation of versal deformations", J. Algebra 255 (2002), no. 2, p. 489-515. | Zbl | MR | DOI

[12] P. Deligne & M. Rapoport - "Les schémas de modules de courbes elliptiques", Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Lecture Notes in Math., vol. 349, Springer, Berlin, 1973, p. 143-316. | MR | Zbl | DOI

[13] P. Deligne - "Théorie de Hodge. III", Publ. Math. Inst. Hautes Études Sci. 44 (1974), p. 5-77. | MR | Zbl | EuDML | mathdoc-id | DOI

[14] M. Demazure & A. Grothendieck - Schémas en groupes, Lecture Notes in Math., vol. 151-153, Springer-Verlag, Berlin, 1970. | Zbl | MR

[15] J. Dieudonné & A. Grothendieck - "Éléments de géométrie algébrique", Publ. Math. Inst. Hautes Études Sci. 4, 8, 11, 17, 20, 24, 28 & 32 (1961-1967). | Zbl

[16] D. Eisenbud - Commutative algebra, Grad. Texts in Math., vol. 150, Springer-Verlag, New York, 1995. | MR | Zbl

[17] T. Ekedahl - "On the multiplicative properties of the de Rham-Witt complex. I", Ark. Mat. 22 (1984), no. 2, p. 185-239. | MR | Zbl | DOI

[18] T. Ekedahl, "On the multiplicative properties of the de Rham-Witt complex. II", Ark Mat. 23 (1985), no. 1, p. 53-102. | MR | Zbl | DOI

[19] G. Faltings - " $p$ -adic Hodge theory", J. Amer. Math. Soc. 1 (1988), no. 1, p. 255-299. | MR | Zbl

[20] G. Faltings, "Crystalline cohomology and $p$ -adic Galois-representations", Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, MD, 1989, p. 25-80. | MR | Zbl

[21] G. Faltings, "Almost étale extensions", Cohomologies $p$ -adiques et applications arithmétiques (II) (J.-M. Berthelot, P. and Fontaine, L. Illusie, K. Kato & M. Rapoport, eds.), Astérisque, vol. 279, Soc. Math. France, Paris, 2002, p. 185-270. | MR | Zbl | mathdoc-id

[22] J.-M. Fontaine - "Sur certains types de représentations $p$ -adiques du groupe de Galois d'un corps local; construction d'un anneau de Barsotti-Tate", Annals of Math. 115 (1982), p. 529-577. | MR | Zbl | DOI

[23] J.-M. Fontaine, "Le corps des périodes $p$ -adiques", Périodes $p$ -adiques, Astérisque, vol. 223, Soc. Math. France, Paris, 1994, p. 59-111. | MR | Zbl | mathdoc-id

[24] J.-M. Fontaine, Représentations $p$ -adiques semi-stables, Astérisque, vol. 223, Soc. Math. France, Paris, 1994. | MR | Zbl | mathdoc-id

[25] J.-M. Fontaine & W. Messing - " $p$ -adic periods and $p$ -adic étale cohomology", Current trends in arithmetical algebraic geometry (Ancata, Calif., 1985), Contemp. Math., vol. 67, Amer. Math. Soc., Providence, RI, 1987, p. 179-207. | MR | Zbl | DOI

[26] P. Gabriel - "Des catégories abéliennes", Bull. Soc. Math. France 90 (1962), p. 323-448. | MR | Zbl | EuDML | mathdoc-id | DOI

[27] J. Giraud - Cohomologie non abélienne, Grundlehren Math. Wiss., vol. 179, Springer-Verlag, Berlin, 1971. | MR | Zbl

[28] A. Grothendieck - Revêtements étales et Groupe Fondamental, Lecture Notes in Math., vol. 224, Springer-Verlag, Berlin, 1971. | MR

[29] A. Grothendieck, Groupes de monodromie en géométrie algébrique (SGA7), Lecture Notes in Math., vol. 288 & 340, Springer-Verlag, Berlin, 1972-1973. | MR

[30] O. Hyodo - "On the de Rham-Witt complex attached to a semi-stable family", Compositio Math. 78 (1991), no. 3, p. 241-260. | MR | Zbl | EuDML | mathdoc-id

[31] O. Hyodo & K. Kato - "Semi-stable reduction and crystalline cohomology with logarithmic poles", Périodes $p$ -adiques (J.-M. Fontaine, éd.), Astérisque, vol. 223, Soc. Math. France, Paris, 1994, p. 221-268. | MR | Zbl | mathdoc-id

[32] L. Illusie - Complexe cotangent et déformations. I, Lecture Notes in Math., vol. 239, Springer-Verlag, Berlin, 1971. | MR | Zbl

[33] L. Illusie, Complexe cotangent et déformations. II, Lecture Notes in Math., vol. 283, Springer-Verlag, Berlin, 1972. | MR | Zbl

[34] L. Illusie, "Complexe de de Rham-Witt et cohomologie cristalline", Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 4, p. 501-661. | MR | Zbl | EuDML | mathdoc-id | DOI

[35] L. Illusie, "Finiteness, duality, and Künneth theorems in the cohomology of the de Rham-Witt complex", Algebraic geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., vol. 1016, Springer, Berlin, 1983, p. 20-72. | MR | Zbl | DOI

[36] L. Illusie & M. Raynaud - "Les suites spectrales associées au complexe de de Rham-Witt", Publ. Math. Inst. Hautes Études Sci. 57 (1983), p. 73-212. | MR | Zbl | EuDML | mathdoc-id | DOI

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

[38] F. W. Kamber & P. Tondeur - "Invariant differential operators and cohomology of Lie algebra sheaves", Mem. Amer. Math. Soc. 113 (1971). | Zbl

[39] K. Kato - "On $p$ -adic vanishing cycles (application of ideas of Fontaine-Messing)", Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, p. 207-251. | MR | Zbl | DOI

[40] K. Kato, "Logarithmic structures of Fontaine-Illusie", Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, MD, 1989, p. 191-224. | MR | Zbl

[41] K. Kato, "Semi-stable reduction and $p$ -adic étale cohomology", Périodes $p$ -adiques (J.-M. Fontaine, éd.), Astérisque, vol. 223, Soc. Math. France, Paris, 1994, p. 269-293. | MR | Zbl | mathdoc-id

[42] K. Kato, "Toric singularities", Amer. J. Math. 116 (1994), no. 5, p. 1073-1099. | MR | Zbl | DOI

[43] K. Kato & T. Saito - "On the conductor formula of Bloch", Publ. Math. Inst. Hautes Études Sci. 100 (2004), p. 5-151. | MR | Zbl | EuDML | mathdoc-id | DOI

[44] N. Katz - "Nilpotent connections and the monodromy theorem: applications of a result of Turrittin", Publ. Math. Inst. Hautes Études Sci. 39 (1970), p. 175-232. | MR | Zbl | EuDML | mathdoc-id

[45] S. L. Kleiman - "Algebraic cycles and the Weil conjectures", Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968, p. 359-386. | MR | Zbl

[46] D. Knutson - Algebraic spaces, Lecture Notes in Math., vol. 203, Springer-Verlag, Berlin, 1971. | MR | Zbl

[47] A. Langer & T. Zink - "De Rham-Witt cohomology for a proper and smooth morphism", J. Inst. Math. Jussieu 3 (2004), no. 2, p. 231-314. | MR | Zbl | DOI

[48] Y. Laszlo & M. C. Olsson - "The six operations for sheaves on Artin stacks I: Finite Coefficients", 2005, preprint, http://arxiv.org/abs/math/0512097. | MR | Zbl | mathdoc-id

[49] G. Laumon & L. Moret-Bailly - Champs algébriques, Ergeb. Math. Grenzgeb. (3), vol. 39, Springer-Verlag, Berlin, 2000. | MR | Zbl

[50] P. Lorenzon - "Indexed algebras associated to a log structure and a theorem of $p$ -descent on log schemes", Manuscripta Math. 101 (2000), no. 3, p. 271-299. | MR | Zbl | DOI

[51] P. Lorenzon, "Logarithmic Hodge-Witt forms and Hyodo-Kato cohomology", J. Algebra 249 (2002), no. 2, p. 247-265. | MR | Zbl | DOI

[52] C. Nakayama - "Nearby cycles for log smooth families", Compositio Math. 112 (1998), no. 1, p. 45-75. | MR | Zbl | DOI

[53] W. Niziol - "Crystalline conjecture via $K$ -theory", Ann. Sci. École Norm. Sup. (4) 31 (1998), no. 5, p. 659-681. | MR | Zbl | EuDML | mathdoc-id | DOI

[54] W. Niziol, "Semistable conjecture via $K$ -theory", 2005, preprint. | MR | Zbl

[55] W. Niziol, "Toric singularities: log-blow-ups and global resolutions", J. Algebraic Geom. 15 (2006), no. 1, p. 1-29. | MR | Zbl | DOI

[56] A. Ogus - "Lectures on logarithmic algebraic geometry", book in preparation; version of 09-15-2006. | MR

[57] A. Ogus, " $F$ -crystals and Griffiths transversality", Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977) (Tokyo), Kinokuniya Book Store, 1978, p. 15-44. | MR | Zbl

[58] A. Ogus, $F$ -crystals, Griffiths transversality, and the Hodge decomposition, Astérisque, vol. 221, Soc. Math. France, Paris, 1994. | MR | Zbl | mathdoc-id

[59] A. Ogus, " $F$ -crystals on schemes with constant log structure", Compositio Math. 97 (1995), no. 1-2, p. 187-225, special issue in honour of Frans Oort. | MR | Zbl | EuDML | mathdoc-id

[60] A. Ogus, "Logarithmic de Rham cohomology", 2000, preprint.

[61] A. Ogus, "Higgs cohomology, $p$ -curvature, and the Cartier isomorphism", Compos. Math. 140 (2004), no. 1, p. 145-164. | MR | Zbl | DOI

[62] M. C. Olsson - "Logarithmic geometry and algebraic stacks", Ann. Sci. École Norm. Sup. (4) 36 (2003), no. 5, p. 747-791. | MR | Zbl | EuDML | mathdoc-id | DOI

[63] M. C. Olsson, "A stacky semi-stable reduction theorem", Int. Math. Res. Not. 29 (2004), p. 1497-1509. | MR | Zbl | DOI

[64] M. C. Olsson, "The logarithmic cotangent complex", Math. Ann. 333 (2005), no. 4, p. 859-931. | MR | Zbl | DOI

[65] M. C. Olsson, "On proper coverings of Artin stacks", Adv. Math. 198 (2005), no. 1, p. 93-106. | MR | Zbl | DOI

[66] M. C. Olsson, "Deformation theory of representable morphisms of algebraic stacks", Math. Z. 253 (2006), no. 1, p. 25-62. | MR | Zbl | DOI

[67] M. C. Olsson, "Hom-stacks and restriction of scalars", Duke Math. J. 134 (2006), no. 1, p. 139-164. | MR | Zbl | DOI

[68] M. C. Olsson, "Sheaves on Artin stacks", J. Reine Angew. Math. 603 (2007), p. 55-112. | MR | Zbl

[69] M. C. Olsson & J. Starr - "Quot functors for Deligne-Mumford stacks", Comm. Algebra 31 (2003), no. 8, p. 4069-4096. | MR | Zbl | DOI

[70] M. Rapoport & T. Zink - "Über die lokale Zetafunktion von Shimuravarietäten. Monodromiefiltration und verschwindende Zyklen in ungleicher Charakteristik", Invent. Math. 68 (1982), no. 1, p. 21-101. | MR | Zbl | EuDML | DOI

[71] J.-P. Serre - Local fields, Grad. Texts in Math., vol. 67, Springer-Verlag, New York, 1979. | MR | Zbl

[72] N. Spaltenstein - "Resolutions of unbounded complexes", Compositio Math. 65 (1988), no. 2, p. 121-154. | MR | Zbl | EuDML | mathdoc-id

[73] T. Tsuji - " $p$ -adic étale cohomology and crystalline cohomology in the semi-stable reduction case", Invent. Math. 137 (1999), no. 2, p. 233-411. | MR | Zbl | DOI

[74] T. Tsuji, "Semi-stable conjecture of Fontaine-Jannsen: a survey", Cohomologies $p$ -adiques et applications arithmétiques (II) (P. Berthelot, J.-M. Fontaine, L. Illusie, K. Kato & M. Rapoport, eds.), Astérisque, vol. 279, Soc. Math. France, Paris, 2002, p. 323-370. | MR | Zbl | mathdoc-id

[75] I. Vidal - "Monodromie locale et fonctions Zêta des log schémas", Geometric Aspects of Dwork Theory, W. de Gruyter, 2004, p. 983-1038. | MR | Zbl