Article Dans Une Revue Compositio Mathematica Année : 2016

The remaining cases of the Kramer–Tunnell conjecture

Résumé

For an elliptic curve $E$ over a local field $K$ and a separable quadratic extension of $K$, motivated by connections to the Birch and Swinnerton-Dyer conjecture, Kramer and Tunnell have conjectured a formula for computing the local root number of the base change of $E$ to the quadratic extension in terms of a certain norm index. The formula is known in all cases except some when $K$ is of characteristic $2$, and we complete its proof by reducing the positive characteristic case to characteristic $0$. For this reduction, we exploit the principle that local fields of characteristic $p$ can be approximated by finite extensions of $\mathbb{Q}_p$--we find an elliptic curve $E'$ defined over a $p$-adic field such that all the terms in the Kramer-Tunnell formula for $E'$ are equal to those for $E$.

Dates et versions

hal-02390991 , version 1 (03-12-2019)

Identifiants

Citer

Kestutis Cesnavicius, Naoki Imai. The remaining cases of the Kramer–Tunnell conjecture. Compositio Mathematica, 2016, 152 (11), pp.2255-2268. ⟨10.1112/S0010437X16007624⟩. ⟨hal-02390991⟩
49 Consultations
0 Téléchargements

Altmetric

Partager

  • More