@incollection{AST_2002__279__271_0,
author = {Illusie, Luc},
title = {An overview of the work of {K.} {Fujiwara,} {K.} {Kato,} and {C.} {Nakayama} on logarithmic \'etale cohomology},
booktitle = {Cohomologies $p$-adiques et applications arithm\'etiques (II)},
editor = {Berthelot Pierre and Fontaine Jean-Marc and Illusie Luc and Kato Kazuya and Rapoport Michael},
series = {Ast\'erisque},
pages = {271--322},
year = {2002},
publisher = {Soci\'et\'e math\'ematique de France},
number = {279},
mrnumber = {1922832},
zbl = {1052.14005},
language = {en},
url = {https://www.numdam.org/item/AST_2002__279__271_0/}
}
TY - CHAP AU - Illusie, Luc TI - An overview of the work of K. Fujiwara, K. Kato, and C. Nakayama on logarithmic étale cohomology BT - Cohomologies $p$-adiques et applications arithmétiques (II) AU - Collectif ED - Berthelot Pierre ED - Fontaine Jean-Marc ED - Illusie Luc ED - Kato Kazuya ED - Rapoport Michael T3 - Astérisque PY - 2002 SP - 271 EP - 322 IS - 279 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_2002__279__271_0/ LA - en ID - AST_2002__279__271_0 ER -
%0 Book Section %A Illusie, Luc %T An overview of the work of K. Fujiwara, K. Kato, and C. Nakayama on logarithmic étale cohomology %B Cohomologies $p$-adiques et applications arithmétiques (II) %A Collectif %E Berthelot Pierre %E Fontaine Jean-Marc %E Illusie Luc %E Kato Kazuya %E Rapoport Michael %S Astérisque %D 2002 %P 271-322 %N 279 %I Société mathématique de France %U https://www.numdam.org/item/AST_2002__279__271_0/ %G en %F AST_2002__279__271_0
Illusie, Luc. An overview of the work of K. Fujiwara, K. Kato, and C. Nakayama on logarithmic étale cohomology, dans Cohomologies $p$-adiques et applications arithmétiques (II), Astérisque, no. 279 (2002), pp. 271-322. https://www.numdam.org/item/AST_2002__279__271_0/
[Br-M] and , Torsion étale cohomology and semi-stable reduction, these Proceedings.
[Bry] , Cohomologie d'intersection et faisceaux pervers, Séminaire Bourbaki 1981/82, n° 585, 129-157, Astérisque 92-93, 1982. | MR | EuDML | Zbl | Numdam
[D1] , La conjecture de Weil, I, Publ. Math. IHES 43 (1974), 273-308. | MR | Zbl | EuDML | Numdam | DOI
, La conjecture de Weil, II, Publ. Math. IHES 52 (1980), 137-252. | MR | Zbl | EuDML | Numdam | DOI
[D2] , Décompositions dans la catégorie dérivée, Proc. of Symposia in Pure Math. 55 (1994), Part I, 115-128, AMS 1994. | MR | Zbl | DOI
[dJ] , Smoothness, Semi-stability and Alterations, Pub. Math. IHES 83 (1996), 51-93. | MR | Zbl | EuDML | Numdam | DOI
[F] , Etale topology and the philosophy of log, Algebraic Geometry Symposium (Kinosaki), 1990, 116-123 (in Japanese).
[F-K] and , Logarithmic étale topology theory, (incomplete) preprint, 1995.
[Fu] , Introduction to toric varieties, Ann. of Math. Studies 131, Princeton Univ. Press, 1993. | MR | Zbl
[Ga] , Approaches to absolute cohomological purity, lecture in Toulouse, July 1, 1994.
[G-M] and , The tame fundamental group of a formal neighborhood of a divisor with normal crossings on a scheme, SLN 208, Springer-Verlag, 1971. | MR | Zbl
[I1] , Logarithmic spaces (according to K. Kato), in Barsotti Symposium in Algebraic Geometry (V. Cristante and W. Messing, Eds.), Perspectives in Math. 15, 183-203, Academic Press, 1994. | MR | Zbl | DOI
[I2] , Autour du théorème de monodromie locale, in Périodes -adiques, Séminaire de Bures, 1988 (Ed. J.-M. Fontaine), 9-57, Astérisque 223, 1994. | MR | Zbl | Numdam
[I3] , Logarithmic smoothness and vanishing cycles, Prépublication univ. Paris-Sud 95-83, 1995.
[Ka 1] , Logarithmic structures of Fontaine-Illusie, in Algebraic Analysis, Geometry and Number Theory, The Johns Hopkins University Press (1989), 191-224. | MR | Zbl
[Ka 2] , Logarithmic degeneration and Dieudonné theory, preprint, 1989.
[Ka 3] , Logarithmic structures of Fontaine-Illusie II, Logarithmic flat topology, (incomplete) preprint, 1991. | MR | Zbl
[Ka 4] , Toric singularities, Amer. J. Math. 116 (1994), 1073-1099. | MR | Zbl | DOI
[Ka 5] , Log proper base change theorem and log smooth base change theorem, preliminary notes, 1995.
[Ka 6] , Constructibility, proper smooth base change, preliminary notes, 1995.
[Ka 7] , Description of , preliminary notes, 1995.
[KKMS] , , , , Toroidal embeddings I, SLN 339, Springer-Verlag, 1973. | MR | Zbl
[K-N] and , Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over , Kodai Math. J. 22 (1999), 161-186. | MR | Zbl | DOI
[Kaw-Nam] and , Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties, Inv. Math. 118 (1994), 395-409. | MR | Zbl | EuDML | DOI
[Ki 1] , Prime to fundamental groups and tame Galois actions, Ann. Inst. Fourier (Grenoble) 50, 4(2000), 1099-1126. | MR | Zbl | EuDML | Numdam | DOI
[Ki 2] , Endomorphisms of logarithmic schemes, preprint, 1999. | MR | Numdam | Zbl
[Na 1] , Logarithmic étale cohomology, Math. Ann. 308 (1997), 365-404. | MR | Zbl | DOI
[Na 2] , Nearby cycles for log smooth families, Comp. Math. 112 (1998), 45-75. | MR | Zbl | DOI
[Na 3] , Degeneration of -adic weight spectral sequences, Amer. J. Math. 122 (2000), 721-733. | MR | Zbl | DOI
[Ni] , Toric singularities, log blow-ups and global resolutions, preprint, 1999. | MR | Zbl
[Od] , Convex Bodies and Algebraic Geometry, An Introduction to the Theory of Toric Varieties, Erg. der Math. Bd 15, Springer-Verlag, 1988. | MR | Zbl | EuDML
[Og] , Logarithmic de Rham cohomology, preprint, 1997.
[R-Z] and , Üeber die lokale Zetafunktion von Shimuravarietäten, Monodromiefiltration und verschwindende Zyklen in ungleicher Charakteristik, Inv. Math. 68 (1982), 21-101. | MR | Zbl | EuDML | DOI
[Sa] , Modules de Hodge polarisables, Pub. RIMS, Kyoto Univ. 24 (1988), 849-995. | MR | Zbl | DOI
[Sa-Z] and , The kernel spectral sequence of vanishing cycles, Duke Math. J. 61 (1990), 329-339. | MR | Zbl | DOI
[S-T] and , Good reduction of abelian varieties, Ann. of Math. 88 (1968), 492-517. | MR | Zbl | DOI
[Ste 1] , Limits of Hodge structures, Inv. Math. 31 (1976), 229-257. | MR | Zbl | EuDML | DOI
[Ste 2] , Logarithmic embeddings of varieties with normal crossings and mixed Hodge structures, Math. Ann. 301 (1995), 105-118. | MR | Zbl | EuDML | DOI
[Tsu] , Semi-stable conjecture of Fontaine-Jannsen: a survey, these Proceedings.
[Vi 1] , Morphismes log étales et descente par homéomorphismes universels, preprint, 1999. | MR | Zbl
[Vi 2] , Descente de Kummer log étale, log régularité et groupe fondamental logarithmique, preliminary notes, 1999.
[Vi 3] , On the local monodromy and zeta functions of log schemes, work in preparation. | Zbl
[Vi 4] , Morphismes log étales et descente par homéomorphismes universels, C. R. Acad. Sei. Paris, t. 332, Série I, 239-244, 2001. | MR | Zbl
[EGA IV] (avec la collaboration de ), Eléments de géométrie algébrique, IV Étude locale des schémas et des morphismes de schémas, Pub. Math. IHÉS 20 (1964), | MR | Zbl | EuDML | Numdam
(avec la collaboration de ), Eléments de géométrie algébrique, IV Étude locale des schémas et des morphismes de schémas, Pub. Math. IHÉS 24 (1965), | MR | Zbl | EuDML | Numdam
(avec la collaboration de ), Eléments de géométrie algébrique, IV Étude locale des schémas et des morphismes de schémas, Pub. Math. IHÉS 28 (1966), | MR | Zbl | EuDML | Numdam
(avec la collaboration de ), Eléments de géométrie algébrique, IV Étude locale des schémas et des morphismes de schémas, Pub. Math. IHÉS 32 (1967). | Zbl | EuDML | Numdam
[SGA 1] Revêtements étales et groupe fondamental, Séminaire de géométrie algébrique du Bois-Marie 1960-61, dirigé par A. Grothendieck, SLN 224, Springer-Verlag, 1971. | MR | Zbl
[SGA 4] Théorie des topos et cohomologie étale des schémas, Séminaire de géométrie algébrique du Bois-Marie 1963-64, dirigé par M. Artin, A. Grothendieck, J.-L. Verdier, SLN 269, 270, 305, Springer-Verlag, 1972, 1973. | MR | Zbl
[SGA 5] Cohomologie -adique et fonctions , Séminaire de géométrie algébrique du Bois-Marie 1965-66, dirigé par A. Grothendieck, SLN 589, Springer-Verlag, 1977. | Zbl
[SGA 7] Groupes de monodromie en géométrie algébrique, Séminaire de géométrie algébrique du Bois-Marie 1967-69, I, dirigé par A. Grothendieck, II par P. Deligne et N. Katz, SLN 288, 340, Springer-Verlag, 1972, 1973. | MR | Zbl
[SGA 4 1/2] Cohomologie étale, par , SLN 569, Springer-Verlag, 1977. | MR | Zbl







