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.
@article{JTNB_2003__15_1_179_0, author = {Guido Kings}, 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}, pages = {179--198}, publisher = {Universit\'e Bordeaux I}, volume = {15}, number = {1}, year = {2003}, zbl = {1050.11063}, mrnumber = {2019010}, language = {en}, url = {https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_179_0/} }
TY - JOUR AU - Guido Kings TI - The Bloch-Kato conjecture on special values of $L$-functions. A survey of known results JO - Journal de théorie des nombres de Bordeaux PY - 2003 SP - 179 EP - 198 VL - 15 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_179_0/ LA - en ID - JTNB_2003__15_1_179_0 ER -
%0 Journal Article %A Guido Kings %T The Bloch-Kato conjecture on special values of $L$-functions. A survey of known results %J Journal de théorie des nombres de Bordeaux %D 2003 %P 179-198 %V 15 %N 1 %I Université Bordeaux I %U https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_179_0/ %G en %F JTNB_2003__15_1_179_0
Guido Kings. 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. https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_179_0/
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