Geodesic
Heights via $p$-Adic Points
Informatics and Automation, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 46-58

Voir la notice de l'article provenant de la source Math-Net.Ru

In a paper published in 1980, the author gave an adelic Tamagawa number interpretation for the Birch and Swinnerton-Dyer conjecture for divisors on abelian varieties. Some years later, in joint work with K. Kato, a more general adelic volume interpretation for zeta values of motives with weights ${}\,{-1}$ was proposed. In the paper at hand, the adelic volume Tamagawa number conjecture is generalized to deal with weight $-1$. As in the paper with Kato, adelic points of varieties are replaced by cohomology with adelic coefficients. Further, we introduce adelic tori over the adelic cohomology groups to mimic the Néron–Severi tori in the 1980 paper. 
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     author = {Spencer Bloch},
     title = {Heights via $p${-Adic} {Points}},
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Spencer Bloch. Heights via $p$-Adic Points. Informatics and Automation, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 46-58. http://geodesic.mathdoc.fr/item/TRSPY_2023_320_a2/