The Bloch-Kato conjecture on special values of L-functions. A survey of known results
Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 1, p. 179-198

This paper contains an overview of the known cases of the Bloch-Kato conjecture. It does not attempt to overview the known cases of the Beilinson conjecture and also excludes the Birch and Swinnerton-Dyer point. The paper starts with a brief review of the formulation of the general conjecture. The final part gives a brief sketch of the proofs in the known cases.

Cet article présente un survol des cas connus de la conjecture de Bloch-Kato. Nous ne cherchons pas à passer en revue tous les cas connus de la conjecture de Beilinson, et nous laissons de côté la conjecture de Birch et Swinnerton-Dyer. L'article commence par une description de la conjecture générale. À la fin, nous indiquons brièvement les démonstrations des cas connus.

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     author = {Kings, Guido},
     title = {The Bloch-Kato conjecture on special values of $L$-functions. A survey of known results},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     pages = {179-198},
     zbl = {1050.11063},
     mrnumber = {2019010},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2003__15_1_179_0}
}
Kings, Guido. The Bloch-Kato conjecture on special values of $L$-functions. A survey of known results. Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 179-198. http://www.numdam.org/item/JTNB_2003__15_1_179_0/

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