Weights in rigid cohomology applications to unipotent F -isocrystals

Bruno Chiarellotto

Annales scientifiques de l'École Normale Supérieure (1998)

  • Volume: 31, Issue: 5, page 683-715
  • ISSN: 0012-9593

How to cite


Chiarellotto, Bruno. "Weights in rigid cohomology applications to unipotent $F$-isocrystals." Annales scientifiques de l'École Normale Supérieure 31.5 (1998): 683-715. <http://eudml.org/doc/82475>.

author = {Chiarellotto, Bruno},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {rigid cohomology; unipotent isocrystals; characteristic ; absolute Frobenius; de Jong alterations; Gysin isomorphism},
language = {eng},
number = {5},
pages = {683-715},
publisher = {Elsevier},
title = {Weights in rigid cohomology applications to unipotent $F$-isocrystals},
url = {http://eudml.org/doc/82475},
volume = {31},
year = {1998},

AU - Chiarellotto, Bruno
TI - Weights in rigid cohomology applications to unipotent $F$-isocrystals
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1998
PB - Elsevier
VL - 31
IS - 5
SP - 683
EP - 715
LA - eng
KW - rigid cohomology; unipotent isocrystals; characteristic ; absolute Frobenius; de Jong alterations; Gysin isomorphism
UR - http://eudml.org/doc/82475
ER -


  1. [BER1] P. BERTHELOT, Finitude et pureté en cohomologie rigide. Inv. Math. 128, 1997, pp. 329-377. Zbl0908.14005MR98j:14023
  2. [BER2] P. BERTHELOT, Cohomologie rigide et cohomologie rigide à support propre. Prepubl. 96-03. I.R.M.A.R., Rennes 1996. 
  3. [B-O] P. BERTHELOT and A. OGUS, F-isocrystals and the de Rham cohomology. Inv. Math. 72, 1983, pp. 159-199. Zbl0516.14017MR85e:14025
  4. [BGR] S. BOSCH, U., GUNTZER and R. REMMERT, Non archimedean analysis. Grundlehren der Math. Wissenshaften 261. Springer-Verlag 1984. Zbl0539.14017MR86b:32031
  5. [BR-Z] J. L. BRYLINSKI and S. ZUCKER, An overview of recent advances in Hodge theory. In Encyclopaedia of Math. Sciences vol.69. Several Complex Variables VI (Barth W., Narasimhan R. Eds.) Springer-Verlag 1990, pp. 39-142. Zbl0793.14005MR91m:14010
  6. [C] K.-T. CHEN, Iterated path integral. Bull.AMS 83, 1977, pp. 831-879. Zbl0389.58001MR56 #13210
  7. [CH-M] G. CHRISTOL and Z. MEBKHOUT, Sur le théorème d'indice des équations différentielles p-adiques III. Preprint 1994. 
  8. [CR] R. CREW, F-isocrystals and their monodromy groups. Ann. Scient. Éc. Norm. Sup. Ser. IV, tome 25, 1992, pp. 429-464. Zbl0783.14008MR94a:14021
  9. [DE1] P. DELIGNE, Théorie de Hodge I. Actes, Congr. Intern. Math. Nice 1970, pp. 425-430. II, Publ. Math. I.H.E.S. 40, 1971, pp. 5-58. III, Publ. Math. I.H.E.S. 44, 1974, pp. 5-77. Zbl0237.14003
  10. [DE2] P. DELIGNE, La conjecture de Weil I. Publ. Math. I.H.E.S. 43, 1974, pp. 273-308. II, Publ. Math. I.H.E.S. 52, 1980, pp. 137-252. Zbl0456.14014MR83c:14017
  11. [DE3] P. DELIGNE, Le groupe fondamental de la droite projective moins trois points. In Ihara, Y., Ribet, K., Serre, J.P. (eds.) : Galois groups over Q, Math. M.S.R.I. Publ. 16, Springer-Verlag 1989, pp. 79-297. Zbl0742.14022MR90m:14016
  12. [DM] P. DELIGNE, and J. S. MILNE, Tannakian categories. In Hodge cycles, Motives and Shimura varieties (Deligne, P., Milne, J.S., Ogus, A., Shih, K.Y. Eds.) L.N.M. 900, Springer-Verlag 1982, pp. 101-228. Zbl0477.14004MR84m:14046
  13. [D-G] M. DEMAZURE and P. GABRIEL, Groupes algébriques. Tome I. North-Holland 1970. Zbl0203.23401
  14. [E] R. ELKIK, Solutions d'équations à coefficients dans un anneau hensélien. Ann. Scient. Ec. Norm. Sup. 6, 1973, pp. 553-604. Zbl0327.14001MR49 #10692
  15. [FA] G. FALTINGS, F-isocrystals on open varieties. Results and conjectures. In Cartier, P. et al. (eds.) The Grothendieck Festschrift, vol. II. Birkhauser 1990, pp. 219-248. Zbl0736.14004MR92f:14015
  16. [FRE] J. FRESNEL, Géometrie analytique rigide. Université de Bordeaux I. Math. Pures 1983/1984. 
  17. [H-Z1] R. HAIN and S. ZUCKER, Unipotent variations of mixed Hodge structure. Inv. Math. 88, 1987, pp. 83-124. Zbl0622.14007MR88i:32035
  18. [H-Z2] R. HAIN and S. ZUCKER, A guide to unipotent variations of mixed Hodge structure. In Hodge Theory Proceedings, Sant Cugat 1985. LNM vol. 1246, Springer, 1987, pp. 92-106. Zbl0622.14008MR88h:14009
  19. [K-M] N. M. KATZ and W. MESSING, Some consequences of the Riemann hypothesis for varieties over finite field. Inv. Math. 23, 1974, pp. 73-77. Zbl0275.14011MR48 #11117
  20. [LS-C] B. LE STUM and B. CHIARELLOTTO, F-Isocristaux unipotents. Prepubl. 96-19, I.R.M.A.R., Rennes 1996. To appear in Comp. Math. Zbl0936.14017
  21. [LS-C1] B. LE STUM and B. CHIARELLOTTO, Pentes en cohomologie rigide et F-isocristaux unipotents. Preprint, 1998. 
  22. [SC] W. SCHMID, Variation of Hodge structure : the singularities of the period mapping. Inv. Math. 22, 1973, pp. 211-319. Zbl0278.14003MR52 #3157
  23. [S] N. SAAVEDRA, Catégories tannakiennes. L.N.M. 265, Springer-Verlag 1972. MR49 #2769
  24. [SGA1] A. GROTHENDIECK et al., Revêtements étales et groupe fondamental. L.N.M. 224. Springer-Verlag 1971. Zbl0234.14002MR50 #7129
  25. [VdP] M. Van der PUT, The cohomology of Monsky-Washnitzer. In Introduction aux cohomologies p-adiques. Memoires de la Société Math. de France. N.23, 1986, pp. 33-60. Zbl0606.14018MR88a:14022
  26. [W] J. WILDESHAUS, Realizations of polylogarithms. L.N.M. 1650. Springer-Verlag 1997. Zbl0877.11001MR98j:11045

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