Altérations de variétés algébriques

Berthelot, Pierre

Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 815, 39 p.

[EGA] A. Grothendieck, Éléments de Géométrie Algébrique, Publ. Math. IHES 24 (1965). | Numdam | Zbl

[SGA 4] M. Artin, A. Grothendieck, J.-L. Verdier, Théorie des topos et cohomologie étale des schémas, t. 3, Lecture Notes in Math. 305, Springer-Verlag (1973). | MR | Zbl

[SGA 7] A. Grothendieck, M. Raynaud, D. S. Rim, Groupes de monodromie en Géométrie Algébrique, t. 1, Lecture Notes in Math. 288, Springer-Verlag (1972). | MR | Zbl

[1] D. Abramovich, A.J. De Jong, Smoothness, semi-stability and toroidal geometry, preprint (1996). | MR | Zbl

[2] M. Artin, The implicit function theorem in algebraic geometry, in Algebraic Geometry, Proc. Bombay Coll., Tata Institute, Oxford University Press (1969), 13-34. | MR | Zbl

[3] M. Artin, G. Winters, Degenerate fibers and reduction of curves, Topology 10 (1971), 373-383. | DOI | MR | Zbl

[4] P. Berthelot, Géométrie rigide et cohomologie des variétés algébriques de caractéristique p, Journées d'analyse p-adique (1982),in D. Barsky, Ph. Robba (ed.), Introduction aux cohomologies p-adiques, Bull. Soc. Math. France, Mémoire 23, p. 7-32 (1986). | EuDML | Numdam | MR | Zbl

[5] P. Berthelot, Cohomologie rigide et cohomologie rigide à supports propres, Première partie (version provisoire 1991), Prépublication IRMAR 96-03, Université de Rennes (1996).

[6] P. Berthelot, Finitude et pureté cohomologique en cohomologie rigide, avec un appendice par A J. De Jong, Prépublication IRMAR, 95-35, Université de Rennes (1995). | MR

[7] E. Bierstone, P. Milman, A simple constructive proof of canonical resolution of singularities, in T. Mora, C. Traverso (ed.), Effective methods in Algebraic Geometry, Progress in Math. 94, Birkhäuser (1991), 11-30. | MR | Zbl

[8] F. Bogomolov, T. Pantev, Weak Hironaka theorem, preprint (1996). | DOI | MR | Zbl

[9] S. Bosch, W. Lütkebohmert, Stable reduction and uniformization of abelian varieties I, Math. Annalen 270 (1985), 349-379. | DOI | EuDML | MR | Zbl

[10] G. Christol, Z. Mebkhout, Sur le théorème de l'indice des équations différentielles $p$-adiques III, preprint (1995). | MR | Zbl

[11] P. Deligne, Théorie de Hodge III, Publ. Math. I.H.E.S. 44 (1975), 5-77. | DOI | EuDML | Numdam | MR | Zbl

[12] P. Deligne, Le lemme de Gabber, in L. Szpiro (ed.), Séminaire sur les pinceaux arithmétiques : la conjecture de Mordell, Astérique 127 (1985), 131-150. | Numdam | MR | Zbl

[13] P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus, Publ. Math. I.H.E.S. 36 (1969), 75-109. | DOI | EuDML | Numdam | MR | Zbl

[14] B. Dwork, On the zeta function of a hypersurface: III, Annals of Math. 83 (1966),457-519. | DOI | MR | Zbl

[15] R. Elkik, Solutions d'équations à coefficients dans un anneau hensélien, Ann. Scient. École Norm. Sup. 6 (1973), 553-604. | DOI | EuDML | Numdam | MR | Zbl

[16] G. Faltings, Crystalline cohomology and $p$-adic Galois representations, in J. I. Igusa (ed.), Algebraic Analysis, Geometry and Number Theory, John Hopkins Univ. Press (1989), 25-80. | MR | Zbl

[17] G. Faltings, Crystalline cohomology of semi-stable curves and $p$-adic Galois representations, Journal of Alg. Geom. 1 (1992), 61-82. | MR | Zbl

[18] G. Faltings, The de Rham conjecture, preprint (1993).

[19] J.-M. Fontaine, Le corps des périodes $p$-adiques, in Périodes $p$-adiques, Séminaire de Bures 1988, Exp. II, Astérique 223 (1994), 59-111. | Numdam | MR | Zbl

[20] J.-M. Fontaine, Représentations $p$-adiques semi-stables, in Périodes $p$-adiques, Séminaire de Bures 1988, Exp. III, Astérique 223 (1994), 113-184. | MR | Zbl

[21] J.-M. Fontaine, W. Messing, $p$-adic periods and $p$-adic étale cohomology, Contemporary Mathematics 67 (1987), 179-207. | DOI | MR | Zbl

[22] W. Fulton, Intersection theory, Ergebnisse der Math. 2, 3. Folge, Springer-Verlag (1984). | MR | Zbl

[23] O. Gabber, Non negativity of Serre's intersection multiplicities, exposé à l'IHES, décembre 1995.

[24] H. Gillet, C. Soulé, $K$-théorie et nullité des multiplicités d'intersection, C. R. Acad. Sc. Paris 300 (1985), 71-74. | MR | Zbl

[25] H. Gillet, C. Soulé, Intersection theory using Adams operations, Inventiones Math. 90 (1987), 243-277. | DOI | EuDML | MR | Zbl

[26] A. Grothendieck, Crystals and the de Rham cohomology of schemes (IHES, Décembre 1966),notes by J. Coates and O. Jussila, in Dix exposés sur la cohomologie des schémas, North-Holland (1968). | MR | Zbl

[27] R. Hartshorne, On the de Rham cohomology of algebraic varieties, Publ. Math. IHES 45 (1976), 5-99. | EuDML | Numdam | MR | Zbl

[28] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero : I, II, Annals of Math. 79 (1964), 109-326. | DOI | MR | Zbl

[29] L. Illusie, Cohomologie de de Rham et cohomologie étale $p$-adique, Séminaire Bourbaki 1989-90, Exp. 726, Astérique 189-190 (1990), 325-374. | EuDML | Numdam | MR | Zbl

[30] L. Illusie, Autour du théorème de monodromie locale, in Périodes $p$-adiques, Séminaire de Bures 1988, Exp. I, Astérique 223 (1994), 9-57. | MR | Zbl

[31] A.J. De Jong, Smoothness, semi-stability and alterations, Preprint 916, University Utrecht (1995), à paraître aux Publ. Math. IHES. | Numdam | MR | Zbl

[32] A.J. De Jong, Families of curves and alterations, preprint (1996). | Numdam | MR | Zbl

[33] J.-P. Jouanolou, Théorèmes de Bertini et applications, Progress in Math. 42, Birkhäuser (1983). | MR | Zbl

[34] K. Kato, Semi-stable reduction and $p$-adic étale cohomology, in Périodes $p$-adiques, Séminaire de Bures 1988, Exp. VI, Astérique 223 (1994), 269-293. | Numdam | MR | Zbl

[35] K. Kato, W. Messing, Syntomic cohomology and $p$-adic étale cohomology, Tôhoku Math. Journal 44 (1992), 1-9. | DOI | MR | Zbl

[36] G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat, Toroidal Embeddings I, Lecture Notes in Math. 339, Springer-Verlag (1973). | MR | Zbl

[37] S. Kleiman, with the collab. of A. Thorup, Intersection theory and enumerative geometry : a decade in review, Proc. of Symp. in Pure Math. 46 (1987), p. 321-370. | DOI | MR | Zbl

[38] F. Knudsen, The projectivity of the moduli space of stable curves, II, III, Math. Scand. 52 (1983), 161-212. | DOI | EuDML | MR | Zbl

[39] D. Knutson, Algebraic spaces, Lecture Notes in Math. 203, Springer-Verlag (1971). | MR | Zbl

[40] H. Matsumura, Commutative Algebra, Benjamin (1970). | MR | Zbl

[41] Z. Mebkhout, A propos du théorème de finitude pour la cohomologie $p$-adique, exposé au Sém. de Géométrie Algébrique, Rennes, mai 1994.

[42] P. Monsky, G. Washnitzer, Formal cohomology: I, Annals of Math. 88 (1968), 181-217. | DOI | MR | Zbl

[43] P. Monsky, Formal cohomology: II. The cohomology sequence of a pair, Annals of Math. 88 (1968), 218-238. | DOI | MR | Zbl

[44] P. Monsky, Finiteness of de Rham cohomology, Amer. Journal of Math. 94 (1972), 237-245. | DOI | MR | Zbl

[45] D. Mumford, J. Fogarty, Geometric Invariant Theory, Ergebnisse der Math. 34, Springer-Verlag (1982). | MR | Zbl

[46] D. Mumford, Stability of projective varieties, L'Ens. Math. 24 (1977), 39-110. | MR | Zbl

[47] C. Nakayama, Nearby cycles for log smooth families, preprint 94-70, Univ. Tokyo (1994). | MR | Zbl

[48] C. Peskine, L. Szpiro, Dimension cohomologique finie et cohomologie locale, Publ. Math. IHES 42 (1973), 47-119. | EuDML | Numdam | MR | Zbl

[49] M. Pikaart, A.J. De Jong, Moduli of curves with non-abelian level structure, in R. Dijkgraaf, C. Faber, G. Van Der Geer (ed.), The moduli spaces of curves, Progress in Math. 129, Birkhäuser (1995), 483-509. | MR | Zbl

[50] H. Popp, Moduli theory and classification theory of algebraic varieties, Lecture Notes in Math. 620, Springer-Verlag (1977). | MR | Zbl

[51] M. Rapoport, T. Zink, Über die lokale Zetafunktion von Shimura-varietäten, Monodromiefiltration und verschwindende Zyklen in ungleicher Characteristik, Inventiones Math. 68 (1982), 21-201. | DOI | EuDML | MR | Zbl

[52] M. Raynaud, L. Gruson, Critères de platitude et de projectivité, Inventiones Math. 13 (1971), 1-89. | DOI | EuDML | MR | Zbl

[53] P. Roberts, The vanishing of intersection multiplicities of perfect complexes, Bull. Amer. Math. Soc. 13 (1985), 127-130. | DOI | MR | Zbl

[54] P. Roberts, Intersection theory and the homological conjectures, Proc. Int. Cong. Math., Kyoto 1990, Springer-Verlag (1991), 361-368. | MR | Zbl

[55] J.-P. Serre, Algèbre locale, Multiplicités, Lecture Notes in Math. 11, Troisième édition, Springer-Verlag (1975). | MR | Zbl

[56] T. Tsuji, Syntomic complexes and $p$-adic vanishing cycles, J. reine angew. Math. 472 (1996), 69-138. | EuDML | MR | Zbl

[57] T. Tsuji, On syntomic cohomology of higher degree of a semi-stable family, preprint 606-01, RIMS, Kyoto (1995).

[58] M. Spivakovsky, Resolution of singularities, preprint (1994).

[59] O. Villamayor, Constructiveness of Hironaka's resolution, Ann. Scient. École Norm. Sup. 22 (1989), 1-32. | DOI | EuDML | Numdam | MR | Zbl