Kyoto Journal of Mathematics

p-Adic period domains and toroidal partial compactifications, I

Kazuya Kato

Full-text: Open access

Abstract

We construct toroidal partial compactifications of p-adic period domains.

Article information

Source
Kyoto J. Math., Volume 51, Number 3 (2011), 561-631.

Dates
First available in Project Euclid: 1 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1312205240

Digital Object Identifier
doi:10.1215/21562261-1299900

Mathematical Reviews number (MathSciNet)
MR2824001

Zentralblatt MATH identifier
1238.14015

Subjects
Primary: 14F30: $p$-adic cohomology, crystalline cohomology
Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10]

Citation

Kato, Kazuya. $p$ -Adic period domains and toroidal partial compactifications, I. Kyoto J. Math. 51 (2011), no. 3, 561--631. doi:10.1215/21562261-1299900. https://projecteuclid.org/euclid.kjm/1312205240


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References

  • [1] A. Ash, D. Mumford, M. Rapoport, and Y. S. Tai, Smooth Compactification of Locally Symmetric Varieties, Lie Groups; History, Frontiers, and Applications, Math. Sci. Press, Brookline, Mass., 1975.
  • [2] A. Beilinson and P. Deligne, “Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs” in Motives (Seattle, 1991), Proc. Sympos. Pure Math. 55, Part 2, Amer. Math. Soc., Providence, 1994, 97–121.
  • [3] P. Berthelot and A. Ogus, F-isocrystals and de Rham cohomology, I, Invent. Math. 72 (1983), 159–199.
  • [4] S. Bloch and K. Kato, “L-functions and Tamagawa numbers of motives” in The Grothendieck Festschrift, Vol. I, Progr. Math. 86, Birkhäuser, Boston, 1990, 333–400.
  • [5] P. Colmez and J.-M. Fontaine, Construction des représentations p-adiques semi-stables, Invent. Math. 140 (2000), 1–43.
  • [6] P. Deligne, La conjecture de Weil, II, Publ. Math. Inst. Hautes Études Sci. 52 (1980), 137–252.
  • [7] J.-M. Fontaine, Le corps des périodes p-adiques, with an appendix by P. Colmez, Astérisque 223 (1994), 59–111.
  • [8] J.-M. Fontaine, “Représentations p-adiques semi-stables,” with an appendix by P. Colmez, in Périodes p-adiques (Bures-sur-Yvette, 1988), Astérisque 223, Soc. Math. France, Montrouge, 1994, 113–184.
  • [9] J.-M. Fontaine and W. Messing, “p-Adic periods and p-adic étale cohomology” in Current Trends in Arithmetical Algebraic Geometry (Arcata, Calif., 1985), Contemp. Math. 67, Amer. Math. Soc., Providence, 1987, 179–207.
  • [10] J.-M. Fontaine, personal communication, 1981.
  • [11] A. Griffiths, Periods of integrals on algebraic manifolds, I: Construction and properties of modular varieties, Amer. J. Math. 90 (1968), 568–626.
  • [12] O. Hyodo and K. Kato, “Semi-stable reduction and crystalline cohomology with logarithmic poles” in Périodes p-adiques (Bures-sur-Yvette, 1988), Astérisque 223, Soc. Math. France, Montrouge, 1994, 221–268.
  • [13] K. Kato, M. Kurihara, and T. Tsuji, Exponential maps of Perrin-Riou and syntomic complexes, preprint, 1996.
  • [14] K. Kato, C. Nakayama, and S. Usui, “Classifying spaces of degenerating mixed Hodge structures, I: Spaces of Borel-Serre orbits” in Algebraic Analysis and Around, Adv. Stud. Pure Math. 54 (2009), 187–222, II: Spaces of SL(2)-orbits, Kyoto J. Math. 51 (2011), 149–261 III: Spaces of nilpotent orbits, preprint.
  • [15] K. Kato, C. Nakayama, and S. Usui, Log intermediate Jacobians, Proc. Japan Acad. Ser. A Math. Sci. 86A (2010), 73–78.
  • [16] K. Kato, C. Nakayama, and S. Usui, Moduli of log mixed Hodge structures, Proc. Japan Acad. Ser. A Math. Sci. 86A (2010), 107–112.
  • [17] K. Kato, C. Nakayama, and S. Usui, Néron models in log mixed Hodge theory by weak fans, Proc. Japan Acad. Ser. A Math. Sci. 86A (2010), 143–148.
  • [18] K. Kato and S. Usui, “Logarithmic structures and classifying spaces (summary)” in The Arithmetic and Geometry of Algebraic Cycles, CRM Proc. Lect. Notes 24 (1999), 115–130.
  • [19] K. Kato and S. Usui, “Borel-Serre spaces and spaces of SL(2)-orbits” in Algebraic Geometry 2000 (Azumino, Japan), Adv. Stud. Pure Math. 36, Math. Soc. Japan, Tokyo, 2002, 321–382.
  • [20] K. Kato and S. Usui, Classifying Spaces of Degenerating Polarized Hodge Structures, Ann. of Math. Stud. 169, Princeton Univ. Press, Princeton, 2008.
  • [21] N. Katz, “Serre-Tate local moduli” in Algeraic Surfaces (Orsay, France, 1976–78), Lecture Notes in Math. 868, Springer, Berlin, 1981, 138–202.
  • [22] M. Kerr and G. Pearlstein, An exponential history of functions with logarithmic growth, preprint, arXiv:0903.4903v2 [math.AG]
  • [23] M. Rapoport, “Non-Archimedean period domains” in Proceedings of the International Congress of Mathematicians, Vols. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, 423–434.
  • [24] M. Rapoport, “Period domains over finite and local fields” in Algebraic Geometry (Santa Cruz, Calif., 1995), Proc. Sympos. Pure Math. 62, Part 1, Amer. Math. Soc., Providence, 1997, 361–381.
  • [25] M. Rapoport and T. Zink, Period Spaces for p-Divisible Groups, Ann. of Math. Stud. 141, Princeton Univ. Press, Princeton, 1996.
  • [26] M. Raskind and X. Xarles, On p-adic intermediate Jacobians, Trans. Amer. Math. Soc. 359 (2007), 6057–6077.
  • [27] W. Schmid, Variation of Hodge structure: The singularities of the period mapping, Invent. Math. 22 (1973), 211–319.
  • [28] S. Usui, Variation of mixed Hodge structures arising from family of logarithmic deformations, II: Classifying space, Duke Math. J. 51 (1984), 851–875.
  • [29] S. Usui, Complex structures on partial compactifications of arithmetic quotients of classifying spaces of Hodge structures, Tohoku Math. J (2) 47 (1995), 405–429.