Abstract

Up to now the Beilinson conjectures gave the values of the leading term of the L-function of an arithmetic variety only up to some non-zero rational number. Bloch & Kato have removed this ambiguity by defining Tamagawa numbers for motives, and Fontaine & Perrin-Rion extended this work to a series of conjectures about mixed motives. Whereas in the Bloch-Kato conjecture there is still some K-theory, this no longer occurs in the work of Fontaine & Perrin-Riou, except possibly in the ultimate definition of a mixed motive. This remains a serious problem.KeywordsAbelian VarietySmooth Projective VarietyMotivic PairMotivic CategoryFinite PlaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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