@article{RSMUP_2012__128__17_0,
author = {Tsuzuki, Nobuo},
title = {A Note on the First Rigid Cohomology Group for Geometrically Unibranch Varieties},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
volume = {128},
year = {2012},
pages = {17-54},
mrnumber = {3076830},
language = {en},
url = {http://dml.mathdoc.fr/item/RSMUP_2012__128__17_0}
}
TSUZUKI, Nobuo. A Note on the First Rigid Cohomology Group for Geometrically Unibranch Varieties. Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012) pp. 17-54. http://gdmltest.u-ga.fr/item/RSMUP_2012__128__17_0/
[1] - - , Theorie des topos et cohomologie etale des schemas (SGA4) , Lecture Notes in Math., 269, 270, and 305, Springer-Verlag, Heidelberg, 1972/3.
[2] - , On Dwork cohomology for singular hypersurfaces , Geometric aspects of Dwork theory. Vol. I, II, pp. 177-244, Walter de Gruyter GmbH & Co. KG, Berlin, 2004. | MR 2023290 | Zbl 1117.14022
[3] - , Algebraic versus rigid cohomology with logarithmic coefficients , Barsotti Symposium in Algebraic Geometry, Perspect. Math., 15, Academic press, San Diego, CA (1994), pp. 11-50. | MR 1307391 | Zbl 0833.14010
[4] , Integration of one-forms on -adic analytic spaces, Annals of Math. Studies 162, Princeton University Press, Princeton, NJ, 2007. | MR 2263704 | Zbl 1161.14001
[5] , Géométrie rigide et cohomologie des variétés algébriques de caractéristique , Introductions aux cohomologies -adiques (Luminy, 1984). Mém. Soc. Math. France (N.S.) No. 23, 3 (1986), pp. 7-32. | Numdam | MR 865810 | Zbl 0606.14017
[6] , Cohomologie rigide et cohomologie rigide à supports propres , Première partie, preprint, 1996.
[7] , Finitude et pureté cohomologique en cohomologie rigide , With an appendix in English by Aise Johan de Jong. Invent. Math. 128, no. 2 (1997), pp. 329-377. | MR 1440308 | Zbl 0908.14005
[8] , Dualité de Poincaré et formule de Künneth en cohomologie rigide , C.R. Acad. Sc. Paris Sér. I Math. 325, no. 5 (1997), pp. 493-498. | MR 1692313 | Zbl 0908.14006
[9] - - , Non-archimedean analysis, Grundlehren der Mathematischen Wissenschaften 261, Springer-Verlag, Berlin, 1984. | MR 746961 | Zbl 0539.14017
[10] - , Overholonomicity of overconvergent -isocrystals over smooth varieties , Annals of Math. 176 , no. 2 (2012), pp. 747-813. | MR 2950764 | Zbl pre06093941
[11] - , Sur la pureté de la cohomologie cristalline , C. R. Acad. Sci. Paris Sér. I Math. 326, no. 8 (1998), pp. 961-963. | MR 1649945 | Zbl 0936.14016
[12] - , -isocristaux unipotents , Compositio Math. 116 , no. 8 (1999), pp. 81-110. | MR 1669440 | Zbl 0936.14017
[13] - , Cohomological descent of rigid cohomology for étale coverings , Rend. Sem. Mat. Univ. Padova 109 (2003), pp. 63-215. | Numdam | MR 1997987 | Zbl 1167.14306
[14] , Deligne's note on Nagata compactifications , J. Ramanujan Math. Soc. 22, no. 3 (2007), pp. 205-257. | MR 2356346 | Zbl 1142.14001
[15] , Solutions d'équations à coefficients dans un anneau hensélien, Ann. Sci. École Norm. Sup. 6 (1973), pp. 553-603. | Numdam | MR 345966 | Zbl 0327.14001
[16] , Revétements étale et groupe fondemental (SGA1) , Lecture Notes in Math. 224 , Springer-Verlag, Heidelberg, 1971. | MR 354651
[17] , Cohomologie locale des faisceaux coherents et theoremes de Lefschetz locaux et globaux (SGA2) , Augmenté d'un exposé par Michéle Raynaud. Séminaire de Géométrie Algébrique du Bois-Marie, 1962. Advanced Studies in Pure Mathematics, Vol. 2. North-Holland Publishing Co., Amsterdam; Masson & Cie, Éditeur, Paris, 1968. | MR 476737 | Zbl 0197.47202
[18] - , Éléments de géométrie algébrique III , Étude cohomologique des faisceaux cohérents, Inst. Hautes Études Sci. Publ. Math. 11 (1961), pp. 5-167; 17 (1963), pp. 5-91. | Numdam | Zbl 0122.16102
[19] - , Éléments de géométrie algébrique IV , Étude locale des schémas et des morphismes de schémas, Inst. Hautes Études Sci. Publ. Math. 20 (1964), pp. 5-259; 24 (1965), pp. 5-231; 32 (1967), pp. 5-361. | Numdam | Zbl 0153.22301
[20] , Smoothness, semi-stability and alterations , Inst. Hautes Études Sci. Publ. Math. 83 (1996), pp. 51-93. | Numdam | MR 1423020 | Zbl 0916.14005
[21] , Semistable reduction for overconvergent -isocrystals , I: Unipotence and logarithmic extensions, Compositio Math. 143, no. 5 (2007), pp. 1164-1212. | MR 2360314 | Zbl 1144.14012
[22] , Imbedding of an abstract variety in a complete variety , J. Math. Kyoto, 2 (1962), pp. 1-10. | MR 142549 | Zbl 0109.39503
[23] , A generalization of the imbedding problem of an abstract variety in a complete variety , J. Math. Kyoto Univ. 3 (1963), pp. 89-102. | MR 158892 | Zbl 0223.14011
[24] , Field theory, Monographs and textbooks in pure and applied mathematics 40, Marcel Dekker Inc. New York and Basel, 1977. | MR 469887 | Zbl 0366.12001
[25] , Weight filtration and slope filtration on the rigid cohomology of a variety in characteristic , to appear in Mém. Soc. Math. France.
[26] , -isocrystals and de Rham cohomology II - convergent isocrystals , Duke Math. J. 51, no. 4 (1984), pp. 765-850. | MR 771383 | Zbl 0584.14008
[27] , Crystalline fundamental groups. II. Log convergent cohomology and rigid cohomology , J. Math. Sci. Univ. Tokyo, 9, no. 1, (2002), pp. 1-163. | MR 1889223 | Zbl 1057.14025
[28] , Relative log convergent cohomology and relative rigid cohomology I , preprint, 2007. http://arxiv.org/abs/0707.1742v2
[29] , Relative log convergent cohomology and relative rigid cohomology II , preprint, 2007. http://arxiv.org/abs/0707.1743v2
[30] , On the Gysin isomorphism of rigid cohomology , Hiroshima Math. J. 29, no. 3 (1999), pp. 479-527. | MR 1728610 | Zbl 1019.14007
[31] , Morphisms of -isocrystals and the finite monodromy theorem for unit-root -isocrystals , Duke Math. J. 111, no. 3 (2002), pp. 385-418. | MR 1885826 | Zbl 1055.14022
[32] , Cohomological descent of rigid cohomology for proper coverings , Invent. Math. 151, no. 1 (2003), pp. 101-133. | MR 1943743 | Zbl 1085.14019
[33] , Cohomological descent in rigid cohomology , Geometric aspects of Dwork theory. Vol. I, II, pp. 931-981, Walter de Gruyter GmbH & Co. KG, Berlin, 2004. | MR 2099093 | Zbl 1073.14026