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Iwasawa theory and $$p$$-adic heights. (Théorie d’Iwasawa et hauteurs $$p$$-adiques.) (French) Zbl 0781.14013
S. Bloch and K. Kato [Grothendieck Festschrift, Vol. 1, Prog. Math. 86, 333–400 (1990; Zbl 0768.14001)] have defined the conjectural formulas for the values of $$L$$-functions attached to the motivic cohomologies of algebraic varieties. The author develops a $$p$$-adic version of this construction theory in the spirit of the Iwasawa theory.

##### MSC:
 14G20 Local ground fields in algebraic geometry 14G40 Arithmetic varieties and schemes; Arakelov theory; heights 11R23 Iwasawa theory 11G50 Heights
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