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4 - Explicit Reciprocity Law of Bloch–Kato and Exponential Maps

Published online by Cambridge University Press:  05 March 2015

By
Anupam Saikia
Edited by
John Coates ,
A. Raghuram ,
Anupam Saikia  and
R. Sujatha
Anupam Saikia
Affiliation:
Indian Institute of Technology Guwahati, India
John Coates
Affiliation:
University of Cambridge
A. Raghuram
Affiliation:
Indian Institute of Science Education and Research, Pune
Anupam Saikia
Affiliation:
Indian Institute of Technology, Guwahati
R. Sujatha
Affiliation:
University of British Columbia, Vancouver
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The Bloch–Kato Conjecture for the Riemann Zeta Function , pp. 65 - 96
Publisher: Cambridge University Press
Print publication year: 2015

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References

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[BO78] Berthelot, P., and Ogus, A. 1978. Notes on Crystalline Cohomology. Princeton University Press.
[BK90] Bloch, S., and Kato, K. 1990. L-functions and Tamagawa numbers of motives. The Grothendieck Festschrift, Vol. I. Progr. Math., 86, 333400. Birkhäuser Boston, Boston, MA.
[BC09] Brinon, O., and Conrad, B. 2009. Notes on p-adic Hodge Theory. CMI Summer School, available online at www.math.stanford.edu/conrad/papers/notes.pdf
[CF67] Cassels, J. W. S., and Frohlich, A. 1967. Algebraic Number Fields. Academic Press.Google Scholar
[Co] Colmez, P. Fontaine's rings and p-adic L-functions. Course given at Tsinghua University (www.math.jussieu.fr/colmez/tsinghua.pdf).
[Fo82] Fontaine, J. M. 1982. 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. (2) 115, no. 3, 529–577.Google Scholar
[FO] Fontaine, J. M., and Ouyang, Y. Theory of p-adic Galois Representations. Book in preparation (www.math.u-psud.fr/fontaine/galoisrep.pdf).
[Gu99] Guo, L. 1999. Hecke characters and formal group characters. Topics in number theory (University Park, PA, 1997). Math. Appl., 467, 181192. Kluwer Acad. Publ., Dordrecht.
[HK03] Huber, A., and Kings, G. 2003. Bloch-Kato conjecture and Main Conjecture of Iwasawa theory for Dirichlet characters. Duke Math. J., 119, no. 3, 393464.Google Scholar
[Iw86] Iwasawa, K. 1986. Local Class Field Theory. Oxford Science Publications.
[Kt93a] Kato, K. 1993. Lectures on the approach to Iwasawa theory for HasseWeil L-functions via BdR. I. Arithmetic algebraic geometry (Trento, 1991). Lecture Notes in Math., 1553, 50163, Springer, Berlin.
[Kt93b] Kato, K. 1993. Iwasawa theory and p-adic Hodge theory. Kodai Math. J., 16, no. 1, 131.Google Scholar
[Mi86] Milne, J. S. 1986. Arithmetic Duality Theorems. Academic Press.
[NSW08] Neukirch, J., Schmidt, A., and Wingberg, K. 2008. Cohomology of Number Fields. Springer.
[Se79] Serre, J. P. 1979. Local fields. Graduate Texts in Mathematics, 67. Springer-Verlag, New York-Berlin.
[Sh87] Shalit, E. 1987. Iwasawa theory of elliptic curves with complex multiplication. Perspectives in Mathematics, 3. Academic Press, Inc., Boston, MA.
[Sh95] Shalit, E. 1995. The explicit reciprocity law of Bloch-Kato. Columbia University Number Theory Seminar (New York, 1992). Astrisque no. 228, 4, 197221.

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