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An analogue of Pfister's local-global principle in the burnside ring

Martin Epkenhans (1999)

Journal de théorie des nombres de Bordeaux

Let N / K be a Galois extension with Galois group 𝒢 . We study the set 𝒯 ( 𝒢 ) of ℤ -linear combinations of characters in the Burnside ring ℬ ( 𝒢 ) which give rise to ℤ -linear combinations of trace forms of subextensions of N / K which are trivial in the Witt ring W ( K ) of K . In particular, we prove that the torsion subgroup of ℬ ( 𝒢 ) / 𝒯 ( 𝒢 ) coincides with the kernel of the total signature homomorphism.

An annihilator for the p -Selmer group by means of Heegner points

Massimo Bertolini (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let E / Q be a modular elliptic curve, and let K be an imaginary quadratic field. We show that the p -Selmer group of E over certain finite anticyclotomic extensions of K , modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic Z p -extension of K . This refines in the current contest a result of [1].

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