Skip to main content
SpringerLink
Log in
Book cover

Arithmetic Algebraic Geometry pp 50–163Cite as

Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR. Part I

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1553))

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Beilinson, A., Higher regulators and values of L-functions, J. Soviet Math. 30 (1985) 2036–2070.

    Article  MATH  Google Scholar 

  2. Beilinson, A., Polylogarithm and cyclotomic elements, preprint.

    Google Scholar 

  3. Bloch, S., Lectures on algebraic cycles, Duke Univ. Math. Series (1980).

    Google Scholar 

  4. Bloch, S. and Kato, K., L-functions and Tamagawa numbers motives, in The Grothendieck Festscherift, Vol. 1 (1980) 334–400.

    MATH  Google Scholar 

  5. Borel, A., Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235–272.

    MathSciNet  MATH  Google Scholar 

  6. Coates, J. and Perrin-Riou, B., On p-adic L-functions attached to motives over Q, in Advanced Studies in Pure Math. 17 (1989) 23–54.

    MathSciNet  MATH  Google Scholar 

  7. Coates J. and Wiles, A., On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977) 223–251.

    Article  MathSciNet  MATH  Google Scholar 

  8. Coleman, R., Division values in local fields, Inv. Math. 53 (1979) 91–116.

    Article  MathSciNet  MATH  Google Scholar 

  9. Damerell, R. M., L-functions of elliptic curves with complex multiplication, I. Acta Arith. 17 (1970) 287–301, II, ibid. 19 (1971) 311–317.

    MathSciNet  MATH  Google Scholar 

  10. Deligne, P., Théorie de Hodge II, Publ. Math. IHES 40 (1972) 5–57.

    Article  MATH  Google Scholar 

  11. Deligne, P., Théorème de finitude en cohomologie l-adique, in Lecture Notes in Math. 569 (SAG 4½), Springer (1977) 233–261.

    Article  MathSciNet  MATH  Google Scholar 

  12. Valeurs de fonctions L et périodes d'intégrales, Proc. Symp. Pure Math., vol. 33, Part 2, AMS (1979) 313–349.

    Google Scholar 

  13. Deligne, P., La conjecture de Weil II, Publ. Math. IHES 52 (1981).

    Google Scholar 

  14. Deligne, P., Le groupe fondamental de la droite projective moins trois points, in Galois groups over Q. Springer (1989) 79–298.

    Google Scholar 

  15. de Shalit, E., The explicit reciprocity law in local class field theory, Duke Math. J. (1986) 163–176.

    Google Scholar 

  16. de Shalit, E., Iwasawa theory of elliptic curves with complex multiplication, Academic Press (1987).

    Google Scholar 

  17. de Shalit, E., The explicit reciprocity law of Bloch and Kato, preprint.

    Google Scholar 

  18. Faltings, G., Crystalline cohomology and p-adic Galois representations, in Algebraic Analysis, Geometry, and Number Theory, Johns Hopkins Univ. (1989) 25–80.

    Google Scholar 

  19. Fontaine, J.-M., Sur certains types de représentations p-adiques du groupe de Galois d'un corps local: construction d'un anneau de Barsotti-Tate, Ann. of Math. 115 (1982) 547–608.

    Article  MathSciNet  Google Scholar 

  20. Fontaine, J.-M., Formes différentielles et modules de Tate des variétés abeliennes sur les corps locaux, Invent. Math. 65 (1982) 379–409.

    Article  MathSciNet  MATH  Google Scholar 

  21. Fontaine, J.-M., Cohomologie crystalline et représentations p-adiques, in Lecture Notes in Math. 1016, Springer (1983) 86–108.

    Google Scholar 

  22. Fontaine, J.-M. and Messing, W., p-adic periods and p-adic étale cohomology, Contemporary Math. 67 (1987) 179–207.

    Article  MathSciNet  MATH  Google Scholar 

  23. Fontaine, J.-M. and Perrin-Riou, B., Autour des conjectures de Bloch et Kato, I. C. R. Acad. Sci. Paris, t. 313, Série I (1991) 189–196, II, ibid., 349–356, III, ibid., 421–428.

    MathSciNet  MATH  Google Scholar 

  24. Fontaine, J.-M. and Perrin-Riou, B., Autour des conjectures de Bloch et Kato, cohomologie galoisienne et valeurs de fonctions L, preprint.

    Google Scholar 

  25. Grothendieck, A., Formule de Lefschetz et rationalité des fonctions L, in Sém. Bourbaki, vol. 1965/66, Benjamin (1966) exposé 306

    Google Scholar 

  26. Illusie, L., Cohomologie de de Rham et cohomologie étale p-adique (Sém. Bourbaki exposé 726), in Astérisque (1990) 325–374.

    Google Scholar 

  27. Jannsen, U., On the l-adic cohomology of varieties over number fields and its Galois cohomology, in Galois groups over Q, Springer (1989) 315–360.

    Google Scholar 

  28. Kato, K., The explicit reciprocity law and the cohomology of Fontaine-Messing, Bull. Soc. Math. France 119 (1991) 397–441.

    MathSciNet  MATH  Google Scholar 

  29. Kato, K., Iwasawa theory and p-adic Hodge theory, preprint.

    Google Scholar 

  30. Kato, K., in preparation.

    Google Scholar 

  31. Kinoshita, J., The twilight-crane (1949). (A drama basing on a Japanese legend.)

    Google Scholar 

  32. Knudsen, F. and Mumford, D., The projectivity of the moduli space of stable curves I, Math. Scand. 39, 1 (1976) 19–55.

    MathSciNet  MATH  Google Scholar 

  33. Kolyvagin, V. A., Euler systems, The Grothendieck Festschrift, vol. 2, Birkhaüser (1990) 435–483.

    MathSciNet  Google Scholar 

  34. Mazur, B., Notes on the étale cohomology of number fields, Ann. Sci. Ec. Norm. Sup. 6 (1973) 521–556.

    MathSciNet  MATH  Google Scholar 

  35. Mazur, B and Wiles, A., Class fields of abelian extensions of Q, Invent. Math. 76 (1984) 179–330.

    Article  MathSciNet  MATH  Google Scholar 

  36. Miyazawa K. (a Japanese poet), A night on the galaxy train (written around 1924).

    Google Scholar 

  37. Quillen, D., Higher algebraic K-theory, I., in Lecture Notes in Math. 341, Springer (1973) 85–147.

    Google Scholar 

  38. Rapoport, M., Schappacher, N. and Schneider, P. (ed.), Beilinson's conjectures on special values of L-functions, Academic Press (1988).

    Google Scholar 

  39. Rubin, K., The "main conjectures" of Iwasawa theory for imaginary quadratic fields, Invent. math. 103 (1991) 25–68.

    Article  MathSciNet  MATH  Google Scholar 

  40. Serre, J.-P., Cohomologie Galoisienne, Lecture Notes in Math. 5, Springer (1965).

    Google Scholar 

  41. Soulé, C., K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Invent. Math. 55 (1979) 251–295.

    Article  MathSciNet  MATH  Google Scholar 

  42. Soulé, C., On higher p-adic regulators, in Lecture Notes in Math. 854, Springer (1981) 371–401.

    Google Scholar 

  43. Soulé, C., The rank of étale cohomology of varieties over p-adic or number fields, Comp. Math. 53 (1984) 113–131.

    MATH  Google Scholar 

  44. Soulé, C., p-adic K-theory of elliptic curves, Duke Math. J. 54 (1987) 249–269.

    Article  MathSciNet  MATH  Google Scholar 

  45. Tate, J., On the conjecture of Birch and Swinnerton-Dyer and a geometric analog, in Sém. Bourbaki, vol. 1965/66, Benjamin (1966) exposé 306.

    Google Scholar 

  46. Tate, J., p-divisible groups, Proceedings of a conference on local fields, Driebergen, 1966, Springer (1967) 158–183.

    Google Scholar 

  47. Washington, L. C., Introduction to cyclotomic fields, Springer (1982).

    Google Scholar 

  48. Weil, A., Elliptic functions according to Eisenstein and Kronecker, Springer (1976).

    Google Scholar 

  49. Weil, A., Number theory: An approach through history; From Hammurapi to Legendre, Birkhäuser (1983).

    Google Scholar 

  50. Wiles, A., Higher explicit reciprocity laws, Ann. Math. 107 (1978) 235–254.

    Article  MathSciNet  MATH  Google Scholar 

  51. Wiles, A., The Iwasawa conjecture for totally real fields, Ann. of Math. 131 (1990) 493–540.

    Article  MathSciNet  MATH  Google Scholar 

  52. Wolfgang, K. S., λ-rings and Adams operators in algebraic K-theory, included in [Ra], 93–102.

    Google Scholar 

  53. Artin, M. and Grothendieck, and Verdier, J. L., Théorie des topos et cohomologie étale des schémas, Lecture Notes in Math. 269, 270, 305, Springer (1972/73).

    Google Scholar 

Download references

Authors
  1. Kazuya Kato
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Edoardo Ballico

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag

About this chapter

Cite this chapter

Kato, K. (1993). Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR. Part I. In: Ballico, E. (eds) Arithmetic Algebraic Geometry. Lecture Notes in Mathematics, vol 1553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084729

Download citation

  • DOI: https://doi.org/10.1007/BFb0084729

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57110-0

  • Online ISBN: 978-3-540-47909-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation