Erratum for: “On the parity of ranks of Selmer groups. III” [cf. Documenta Math. 12 (2007), 243–274]

Abstract

In the manuscript “On the Parity of Ranks of Selmer Groups III” Documenta Math. 12 (2007), 243–274, [1], Remark 4.$1.2(4)$ and the treatment of archimedean $\epsilon$-factors in 4.1.3 are incorrect. Contrary to what is stated in 0.3, the individual archimedean $\epsilon$-factors ${\epsilon }_u(M)(u\mid \infty )$ cannot be expressed, in general, in terms of $M_{\mathfrak{p}}$, but their product can.

Link to the paper corrected hereby.