Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
Manuscript map · lines 2455–2464
OpenAI@2026-10-07#rem:oai-p-002-01
Authors: OpenAI. Family 002.
Title: Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank.
Abstract: We prove the full Birch–Swinnerton-Dyer leading-term formula for every elliptic curve over ℚ whose full q-power Selmer group has corank zero or one at some prime q. The analytic and Mordell–Weil ranks equal that corank, and the Tate–Shafarevich group is finite. The formula includes all prime factors and requires no additional hypotheses on reduction, rational torsion, isogenies, complex multiplication, or residual Galois representations.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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