The two-variable -adic Birch–Swinnerton-Dyer conjecture
The two-variable -adic Birch–Swinnerton-Dyer conjecture
Let , let be the two-variable -adic -function, and let be the augmentation ideal of . Let be the two-variable -adic regulator, let be the interpolation factor for the trivial character, let be the Shafarevich–Tate group, and let be the Tamagawa factors.
Two-variable -adic Birch–Swinnerton-Dyer conjecture. The element lies in and satisfies
\mathbf{L}\equiv c(\chi_{\mathrm{triv}})\\,\\#\Sha(E/K)\\,\prod_v c_v\cdot R_p(E,K)\pmod{\mathbf{I}^{r+1}}.This is the two-variable leading-term formula predicted by the -adic Birch–Swinnerton-Dyer principle. The supplied text gives no resolution.
Sources & referencesView supporting material
Primary source
Barry Mazur and Karl Rubin, “Elliptic curves and class field theory”, arXiv:math/0304235 (2003).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.