Displaying similar documents to “An explicit formula for the Hilbert symbol of a formal group”

Anticyclotomic Iwasawa theory of CM elliptic curves

Adebisi Agboola, Benjamin Howard (2006)

Annales de l’institut Fourier

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We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Z p -extension of the CM field, where p is a prime of good, ordinary reduction for E . When the complex L -function of E vanishes to even order, Rubin’s proof of the two variable main conjecture of Iwasawa theory implies that the Pontryagin dual of the p -power Selmer group over the anticyclotomic extension is a torsion Iwasawa module. When the order of vanishing is odd, work of Greenberg show that it is not a torsion...

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let A , B denote generic binary forms, and let 𝔲 r = ( A , B ) r denote their r -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the { 𝔲 r } . As a consequence, we show that each of the higher transvectants { 𝔲 r : r 2 } is redundant in the sense that it can be completely recovered from 𝔲 0 and 𝔲 1 . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of S L 2 -representations,...