scholarly journals The explicit reciprocity law and the cohomology of Fontaine-Messing

1991 ◽  
Vol 119 (4) ◽  
pp. 397-441 ◽  
Author(s):  
Kazuya Kato
Keyword(s):  
Reciprocity Law ◽  
Explicit Reciprocity Law

An Explicit Reciprocity Law Associated to Some Finite Coverings of Algebraic Curves

2018 ◽  
Vol 15 (3) ◽  
Author(s):  
José M. Muñoz Porras ◽  
Fernando Pablos Romo ◽  
Francisco J. Plaza Martín
Keyword(s):  
Algebraic Curves ◽  
Reciprocity Law ◽  
Explicit Reciprocity Law

scholarly journals ON THE -ADIC VARIATION OF HEEGNER POINTS

2019 ◽  
Vol 19 (6) ◽  
pp. 2127-2164 ◽  
Author(s):  
Francesc Castella
Keyword(s):  
Elliptic Curves ◽  
Selmer Groups ◽  
Direct Relation ◽  
Heegner Points ◽  
Reciprocity Law ◽  
Heegner Cycles ◽  
Hida Families ◽  
Explicit Reciprocity Law

In this paper, we prove an ‘explicit reciprocity law’ relating Howard’s system of big Heegner points to a two-variable $p$-adic $L$-function (constructed here) interpolating the $p$-adic Rankin $L$-series of Bertolini–Darmon–Prasanna in Hida families. As applications, we obtain a direct relation between classical Heegner cycles and the higher weight specializations of big Heegner points, refining earlier work of the author, and prove the vanishing of Selmer groups of CM elliptic curves twisted by 2-dimensional Artin representations in cases predicted by the equivariant Birch and Swinnerton-Dyer conjecture.

scholarly journals On explicit reciprocity law over formal groups

2004 ◽  
Vol 2004 (12) ◽  
pp. 607-635 ◽  
Author(s):  
Shaowei Zhang
Keyword(s):  
Formal Group ◽  
Tempered Distributions ◽  
Formal Groups ◽  
One Dimensional ◽  
Reciprocity Law ◽  
Explicit Reciprocity Law ◽  
Tate Formal Group

Let𝔣be a one-dimensional Lubin-Tate formal group overℤp. Colmez (1998) and Perrin-Riou (1994) proved an explicit reciprocity law for tempered distributions over the formal group𝔾m. In this paper, the general explicit reciprocity law over the formal group𝔣is proved.

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