On the parity of ranks of Selmer groups. III.
On the parity of ranks of Selmer groups. III.
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关于塞尔默团体的等级平等。
作者：
J. Nekovář
备注4.1.2(4)和4.1.3中阿基米德ε因子的处理是不正确的。与 0.3 中所述相反，单个阿基米德 ε 因子 εu(M) (u | ∞) 一般不能用 Mp 表示，但它们的乘积可以。为了激发下面的修正，考虑 F 上的动机 M（纯权重 w），系数在 L 中。设置 S̃∞ = {τ : F ↪→ C}, S̃p = {σ : F ↪→ Qp} 并用 r∞ : S̃∞ −→ S∞, rp : S̃p −→ Sp 表示规范满射。修复嵌入 ι : L ↪→ C 和同构 λ : Qp ∼ −→ C ，使得 p 由 ιp = λ−1 ◦ ι : L ↪→ Qp 诱导。每个 v ∈ Sp 对应一个子集
Remark 4.1.2(4) and the treatment of archimedean ε-factors in 4.1.3 are incorrect. Contrary to what is stated in 0.3, the individual archimedean ε-factors εu(M) (u | ∞) cannot be expressed, in general, in terms of Mp, but their product can. To motivate the corrections below, consider a motive M (pure of weight w) over F with coefficients in L. Set S̃∞ = {τ : F ↪→ C}, S̃p = {σ : F ↪→ Qp} and denote by r∞ : S̃∞ −→ S∞, rp : S̃p −→ Sp the canonical surjections. Fix an embedding ι : L ↪→ C and an isomorphism λ : Qp ∼ −→ C such that p is induced by ιp = λ−1 ◦ ι : L ↪→ Qp. To each v ∈ Sp then corresponds a subset