Around the Poincaré Lemma, After Beilinson

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• 作者：Luc Illusie
• 关键词：De Rham cohomology ; p ; adic étale cohomology ; Fontaine’s rings ; Cotangent complex ; Log scheme ; Alteration ; Semi ; stable morphism ; Grothendieck topology ; 11G25 ; 14F20 ; 14F30 ; 14F40 ; 14K30 ; 18G30 ; 18G55
• 刊名：Acta Mathematica Vietnamica
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：40
• 期：2
• 页码：231-253
• 全文大小：1,035 KB
• 参考文献：1.Beilinson, A.: p-adic periods and de Rham cohomology. J. AMS 25, 715-38 (2012)MATH MathSciNet
  2.Beilinson, A.: On the crystalline period map. Camb. J. of Math. 1(2013), 1-1 (2013). arXiv: 1111.-316 MATH MathSciNet View Article
  3.Bloch, S., Ogus, A.: Gersten’s conjecture and the homology of schemes. Ann. Sci. E.N.S. 7, 181-01 (1974)MATH MathSciNet
  4.De Jong, A.J.: Smoothness, semi-stability and alterations. Pub. Math. IHéS 83, 51-3 (1996)MATH MathSciNet View Article
  5.Deligne, P.: Théorie de Hodge: II. Pub. math. IHéS 40, 5-7 (1971)MATH MathSciNet View Article
  6.Deligne, P.: Théorie de Hodge: III. Pub. math. IHéS 44, 5-7 (1974)MATH MathSciNet View Article
  7.Deligne, P.: Hodge cycles on abelian varieties. In: Hodge Cycles, Motives, and Shimura varieties, 9-100, Lecture Notes in Mathematics 900. Springer-Verlag (1982)
  8.De Rham, G.: ?uvres mathématiques. L’Enseignement mathématique. Université de Genève (1981)
  9.Faltings, G.: Almost étale extensions. Cohomologies p-adiques et applications arithmétiques (II), Astérisque 279, SMF, pp 185-70 (2002)
  10.Faltings, G., Chai, C.-L.: Degeneration of Abelian Varietees. Ergebnisse der Math. und ihrer Grenzgebiete 3. Folge, Band 22. Springer-Verlag (1990)
  11.Fontaine, J.-M.: Formes différentielles et modules de Tate des variétés abéliennes sur les corps locaux. Inv. Math. 65, 379-09 (1982)MATH MathSciNet View Article
  12.Fontaine, J.-M.: Le corps des périodes p-adiques. In Périodes p-adiques, Astérisque 223. SMF, pp 59-01 (1994)
  13.Grothendieck, A.: On the de Rham cohomology of algebraic varieties. Pub. math. IHéS 29, 95-03 (1966)MathSciNet View Article
  14.Illusie, L.: Complexe cotangent et déformations I. Lecture Notes in Mathematics 239. Springer (1971)
  15.Illusie, L.: Complexe cotangent et déformations II. Lecture Notes in Mathematics 283. Springer-Verlag (1972)
  16.Illusie, L.: VI Log régularité, actions très modérées. In Travaux de Gabber sur l’uniformisation locale et la cohomologie étale des schémas quasi-excellents, Séminaire à l’école polytechnique 2006-008, dirigé par Luc Illusie, Yves Laszlo, et Fabrice Orgogozo, avec la collaboration de F. Déglise, A. Moreau, V. Pilloni, M. Raynaud, J. Riou, B. Stroh, M. Temkin et W. Zheng, Astérisque 363-64 (2014)
  17.Kato, K.: Logarithmic structures of Fontaine-Illusie, pp 191-24. Algebraic Analysis, Geometry, and Number Theory, the Johns Hopkins University Press (1988)
  18.Niziol, W.: Semistable conjecture via K-theory. Duke Math. J. 141, 151-78 (2008)MATH MathSciNet View Article
  19.Olsson, M.: The logarithmic cotangent complex. Math. Ann. 333, 859-31 (2005)MATH MathSciNet View Article
  20.Temkin, M.: Stable modification of relative curves. J. Alg. Geom. 19, 603-77 (2010)MATH MathSciNet View Article
  21.Tsuji, T.: p-adic étale cohomology and crystalline cohomology in the semi-stable reduction case. Inv. Math. 137, 233-11 (1999)MATH MathSciNet View Article
  22.Yamashita, G.: Théorie de Hodge p-adique pour les variétés ouvertes. C. R. A. S. 349, 1127-130 (2011)MATH
  
• 作者单位：Luc Illusie (1)
  
  1. Mathématique, Bat. 425, Université Paris-Sud, 91405, Orsay Cedex, France
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144

文摘

The following notes are an expanded version of talks on Beilinson’s paper as reported by Beilinson (J. AMS 25, 715-38, 2012) given at the department of mathematics of the university of Padova on October 25 and 26, 2012, at the Séminaire RéGA (Réseau d’étudiants en Géométrie Algébrique, Institut Henri Poincaré, Paris) on December 12, 2012, lectures at the KIAS (Seoul) on January 3 and 4, 2013, a course at the Morningside Center of Mathematics (Beijing) on February 18, 25, and March 4, 11, 2013, and a course at the VIASM (Hanoi) on September 4, 5, 9, 10, 11, 2014. I do not discuss Beilinson’s next paper as reported by Beilinson (Camb. J. of Math. 1, 1-1, 2013), which deals with refinements of the comparison theorem between p-adic étale cohomology and de Rham cohomology.