The Arithmetic of Elliptic Curves
Book
Domain Context
Number Theory and Analysis
Citation
Joseph H. Silverman. (1986). The Arithmetic of Elliptic Curves. 106. Springer.
Why this reference is included
Silverman’s The Arithmetic of Elliptic Curves (1986), published by Springer, sits in the program’s reference corpus as a standing technical source. Cited across Book II (Categorical Holomorphy), Part 3, Chapter Torus Degeneration and the Geometric Lemniscate; Book II (Categorical Holomorphy), Part 10, Chapter BSD Bridge: Proto-Rationality in Split-Complex Regime — the central framing is “The Full Torus at Finite Depth At every finite stage k of the primorial ladder, the fiber T^2 = S^1_γ × S^1_η (II.D06, Chapter ) is a genuine two-dimensional torus”.
Cited in
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Book II — Categorical Holomorphy Part 3Chapter Torus Degeneration and the Geometric Lemniscate
The Full Torus at Finite Depth At every finite stage k of the primorial ladder, the fiber T^2 = S^1_γ × S^1_η (II.D06, Chapter ) is a genuine two-dimensional torus
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Book II — Categorical Holomorphy Part 10Chapter BSD Bridge: Proto-Rationality in Split-Complex Regime
Elliptic curves. An elliptic curve E / is a smooth projective curve of genus 1 defined over with a specified rational point
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Book II — Categorical Holomorphy Part 10Chapter BSD Bridge: Proto-Rationality in Split-Complex Regime
The group E() of rational points is a finitely generated abelian group by the Mordell–Weil theorem: \[ E() ≅ ^r ⊕ E()_tors, \] where r ≥ 0 is the algebraic rank and E()_tors is the finite torsion subgroup