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.
@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},
     pages = {17--54},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {128},
     year = {2012},
     mrnumber = {3076830},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2012__128__17_0/}
}
TY  - JOUR
AU  - TSUZUKI, Nobuo
TI  - A Note on the First Rigid Cohomology Group for Geometrically Unibranch Varieties
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2012
SP  - 17
EP  - 54
VL  - 128
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_2012__128__17_0/
LA  - en
ID  - RSMUP_2012__128__17_0
ER  - 
%0 Journal Article
%A TSUZUKI, Nobuo
%T A Note on the First Rigid Cohomology Group for Geometrically Unibranch Varieties
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2012
%P 17-54
%V 128
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_2012__128__17_0/
%G en
%F 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://www.numdam.org/item/RSMUP_2012__128__17_0/

[1] M. Artin - A. Grothendieck - J. L. Verdier, Theorie des topos et cohomologie etale des schemas (SGA4) , Lecture Notes in Math., 269, 270, and 305, Springer-Verlag, Heidelberg, 1972/3.

[2] F. Baldassarri - P. Berthelot, 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 | Zbl

[3] F. Baldassarri - B. Chiarellotto, 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 | Zbl

[4] V. G. Berkovich, Integration of one-forms on p -adic analytic spaces, Annals of Math. Studies 162, Princeton University Press, Princeton, NJ, 2007. | MR | Zbl

[5] P. Berthelot, Géométrie rigide et cohomologie des variétés algébriques de caractéristique p , Introductions aux cohomologies p -adiques (Luminy, 1984). Mém. Soc. Math. France (N.S.) No. 23, 3 (1986), pp. 7-32. | Numdam | MR | Zbl

[6] P. Berthelot, Cohomologie rigide et cohomologie rigide à supports propres , Première partie, preprint, 1996.

[7] P. Berthelot, 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 | Zbl

[8] P. Berthelot, 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 | Zbl

[9] S. Bosch - U. Güntzer - R. Remmert, Non-archimedean analysis, Grundlehren der Mathematischen Wissenschaften 261, Springer-Verlag, Berlin, 1984. | MR | Zbl

[10] D. Caro - N. Tsuzuki, Overholonomicity of overconvergent F -isocrystals over smooth varieties , Annals of Math. 176 , no. 2 (2012), pp. 747-813. | MR

[11] B. Chiarellotto - B. Le Stum, Sur la pureté de la cohomologie cristalline , C. R. Acad. Sci. Paris Sér. I Math. 326, no. 8 (1998), pp. 961-963. | MR | Zbl

[12] B. Chiarellotto - B. Le Stum, F -isocristaux unipotents , Compositio Math. 116 , no. 8 (1999), pp. 81-110. | MR | Zbl

[13] B. Chiarellotto - N. Tsuzuki, Cohomological descent of rigid cohomology for étale coverings , Rend. Sem. Mat. Univ. Padova 109 (2003), pp. 63-215. | Numdam | MR | Zbl

[14] B. Conrad, Deligne's note on Nagata compactifications , J. Ramanujan Math. Soc. 22, no. 3 (2007), pp. 205-257. | MR | Zbl

[15] R. Elkik, Solutions d'équations à coefficients dans un anneau hensélien, Ann. Sci. École Norm. Sup. 6 (1973), pp. 553-603. | Numdam | MR | Zbl

[16] A. Grothendieck, Revétements étale et groupe fondemental (SGA1) , Lecture Notes in Math. 224 , Springer-Verlag, Heidelberg, 1971. | MR

[17] A. Grothendieck, 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 | Zbl

[18] A. Grothendieck - J. Dieudonné, 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

[19] A. Grothendieck - J. Dieudonné, 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

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

[21] K. Kedlaya, Semistable reduction for overconvergent F -isocrystals , I: Unipotence and logarithmic extensions, Compositio Math. 143, no. 5 (2007), pp. 1164-1212. | MR | Zbl

[22] M. Nagata, Imbedding of an abstract variety in a complete variety , J. Math. Kyoto, 2 (1962), pp. 1-10. | MR | Zbl

[23] M. Nagata, A generalization of the imbedding problem of an abstract variety in a complete variety , J. Math. Kyoto Univ. 3 (1963), pp. 89-102. | MR | Zbl

[24] M. Nagata, Field theory, Monographs and textbooks in pure and applied mathematics 40, Marcel Dekker Inc. New York and Basel, 1977. | MR | Zbl

[25] Y. Nakkajima, Weight filtration and slope filtration on the rigid cohomology of a variety in characteristic p>0 , to appear in Mém. Soc. Math. France.

[26] A. Ogus, F -isocrystals and de Rham cohomology II - convergent isocrystals , Duke Math. J. 51, no. 4 (1984), pp. 765-850. | MR | Zbl

[27] A. Shiho, Crystalline fundamental groups. II. Log convergent cohomology and rigid cohomology , J. Math. Sci. Univ. Tokyo, 9, no. 1, (2002), pp. 1-163. | MR | Zbl

[28] A. Shiho, Relative log convergent cohomology and relative rigid cohomology I , preprint, 2007. http://arxiv.org/abs/0707.1742v2

[29] A. Shiho, Relative log convergent cohomology and relative rigid cohomology II , preprint, 2007. http://arxiv.org/abs/0707.1743v2

[30] N. Tsuzuki, On the Gysin isomorphism of rigid cohomology , Hiroshima Math. J. 29, no. 3 (1999), pp. 479-527. | MR | Zbl

[31] N. Tsuzuki, Morphisms of F -isocrystals and the finite monodromy theorem for unit-root F -isocrystals , Duke Math. J. 111, no. 3 (2002), pp. 385-418. | MR | Zbl

[32] N. Tsuzuki, Cohomological descent of rigid cohomology for proper coverings , Invent. Math. 151, no. 1 (2003), pp. 101-133. | MR | Zbl

[33] N. Tsuzuki, 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 | Zbl