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The Tate conjecture: Hodge's arithmetic twin, and BSD over function fields
joint
Tate's conjecture (1965) is the Hodge conjecture with Galois representations in place of Hodge structures. For an elliptic surface over a finite field, the Tate conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for its generic fibre (Artin-Tate 1966, Milne 1975), and both to the finiteness of the Brauer group. One conjecture, three faces.
source
Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)
card id
card_joint_tate_conjecture
address
WIT.codex.EXP/the-tate-conjecture-hodge-s-arithmetic-twin-and-/REF.WITNESSED@narrow-highway-the-mille
adjoining cards
- part of → The Millennium floor - seven open questions, and where they connect — a joint that is proven or observed - a part of the floor
- connects at → The Hodge conjecture — The Tate conjecture: Hodge's arithmetic twin, and BSD over function fields. tate 1965; art
- connects at → The Birch and Swinnerton-Dyer conjecture — The Tate conjecture: Hodge's arithmetic twin, and BSD over function fields. tate 1965; art
- cites → J. Tate 1965 — Algebraic cycles and poles of zeta functions — the record the joint stands on
- cites → M. Artin 1966 — On the conjectures of Birch and Swinnerton-Dyer and a geometric analog — the record the joint stands on
- cites → J. S. Milne 1975 — On a conjecture of Artin and Tate — the record the joint stands on
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