{"query": "J. Tate 1965 — Algebraic cycles and poles of zeta functions", "count": 20, "results": [{"id": "card_src_mill_tate_1965", "title": "J. Tate 1965 — Algebraic cycles and poles of zeta functions", "shelf": "millennium", "surface": "secular", "snippet": "J. Tate (1965). Algebraic cycles and poles of zeta functions. Arithmetical Algebraic Geometry (Purdue 1963), Harper & Row, 1965, 93–110. Canonical: https://www.claymath.org/millennium/hodge-conjecture", "authority_tier": "reference", "source": "J. Tate (1965), Arithmetical Algebraic Geometry (Purdue 1963), Harper & Row, 1965, 93–110", "readable": false, "generated": false}, {"id": "card_floor_millennium", "title": "The Millennium floor - seven open questions, and where they connect", "shelf": "codex", "surface": "secular", "snippet": "The seven Millennium Prize Problems on the one map of reality. The FLOOR is what is proven or observed: the joints where two of the questions meet at one established thing - the GUE statistics shared ", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor (operator seed)", "readable": false, "generated": false}, {"id": "card_joint_tate_conjecture", "title": "The Tate conjecture: Hodge's arithmetic twin, and BSD over function fields", "shelf": "codex", "surface": "secular", "snippet": "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 a", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_artin_tate_1966", "title": "M. Artin 1966 — On the conjectures of Birch and Swinnerton-Dyer and a geometric analog", "shelf": "millennium", "surface": "secular", "snippet": "M. Artin, J. Tate (1966). On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. Séminaire Bourbaki 9 (1964–66), exp. 306, 415–440. Canonical: http://www.numdam.org/item/SB_1964-1966_", "authority_tier": "reference", "source": "M. Artin, J. Tate (1966), Séminaire Bourbaki 9 (1964–66), exp. 306, 415–440", "readable": false, "generated": false}, {"id": "card_src_mill_milne_1975", "title": "J. S. Milne 1975 — On a conjecture of Artin and Tate", "shelf": "millennium", "surface": "secular", "snippet": "J. S. Milne (1975). On a conjecture of Artin and Tate. Ann. Math. 102 (1975) 517–533. DOI 10.2307/1971042. Canonical: https://doi.org/10.2307/1971042. No free copy found; cited by its record. License ", "authority_tier": "reference", "source": "J. S. Milne (1975), Ann. Math. 102 (1975) 517–533", "readable": false, "generated": false}, {"id": "card_src_pron_tate", "title": "tate", "shelf": "pronunciation", "surface": "secular", "snippet": "tate: pronounced (ARPABET) T EY1 T. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_src_word_tate", "title": "tate", "shelf": "dictionary", "surface": "secular", "snippet": "tate: (noun) United States poet and critic (1899-1979) — syn: Allen Tate, John Orley Allen Tate", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_allen_tate", "title": "allen tate", "shelf": "dictionary", "surface": "secular", "snippet": "allen tate: (noun) United States poet and critic (1899-1979) — syn: Tate, John Orley Allen Tate", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_john_orley_allen_tate", "title": "john orley allen tate", "shelf": "dictionary", "surface": "secular", "snippet": "john orley allen tate: (noun) United States poet and critic (1899-1979) — syn: Tate, Allen Tate", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_taxon_3715058", "title": "Tates", "shelf": "taxonomy", "surface": "secular", "snippet": "Tates — a genus. In the tree of life under Alysiinae.", "authority_tier": "reference", "source": "NCBI Taxonomy (public domain)", "readable": false, "generated": false}, {"id": "card_src_drug_dota_tate_acetate", "title": "Dota-Tate Acetate", "shelf": "medicine", "surface": "secular", "snippet": "DOTA-TATE acetate: a BULK INGREDIENT, powder.", "authority_tier": "reference", "source": "openFDA / FDA NDC Directory (public domain)", "readable": false, "generated": false}, {"id": "card_src_place_3933266", "title": "Pampa de Tate", "shelf": "geography", "surface": "secular", "snippet": "Pampa de Tate: a place in PE, 11 at -14.145, -75.692, population 5,180. Feature PPL, timezone America/Lima.", "authority_tier": "reference", "source": "GeoNames (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_chain_neron_1965", "title": "Néron 1965 — Quasi-fonctions et hauteurs sur les variétés abéliennes", "shelf": "codex", "surface": "secular", "snippet": "A. Néron (1965). Quasi-fonctions et hauteurs sur les variétés abéliennes. Ann. Math. 82 (1965) 249–331. DOI 10.2307/1970644. Canonical: https://doi.org/10.2307/1970644. Cited by its record. License as", "authority_tier": "reference", "source": "A. Néron (1965), Ann. Math. 82 (1965) 249–331", "readable": false, "generated": false}, {"id": "card_joint_manin_algorithm", "title": "If Sha is finite, the rank is computable", "shelf": "codex", "surface": "secular", "snippet": "Manin (1971): if the Tate-Shafarevich group is finite - part of what BSD asserts - then the rank of an elliptic curve over Q is effectively computable by descent. Without it, no algorithm is known. A ", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_src_etym_smith", "title": "smith", "shelf": "etymology", "surface": "secular", "snippet": "smith: etymology (Webster 1913) — n.: [AS. smi; akin to D. smid, G. schmied, OHG. smid, Icel. smi, Dan. & Sw. smed, Goth. smi (in comp.); cf. Gr. 1. One who forgess with the hammer; one who works in m", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_theory_algebraic_geometry", "title": "Algebraic geometry (solution sets as shapes)", "shelf": "theories", "surface": "secular", "snippet": "Algebraic geometry (solution sets as shapes) — an engine domain that can touch it: mathematics. Calibration: map-only — specific curve computations verify; the theory is abstract. The study of the sha", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_saros_eclipse_cycle", "title": "The Saros cycle (eclipse prediction)", "shelf": "theories", "surface": "secular", "snippet": "The Saros cycle (eclipse prediction) — an engine domain that can touch it: ephemeris. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and seal them. ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_alm_connection_riemann_hypothesis_open_zeta_facts", "title": "Almanac: The Riemann Hypothesis -- an open question about where the zeta function vanishes, with the established facts sealed and the conjecture marked honestly", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The Riemann zeta function, zeta(s) = the sum of 1/k^s, is the deepest known bridge between the smooth world of analysis and the prime numbers. Several of its truths are firmly ESTABLISHED ", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_chart_zeta", "title": "The zeta function", "shelf": "codex", "surface": "secular", "snippet": "The zeta function. A chart on the one map: this is the tick stick stick_the_zeta_function, placed at the node it charts. Basis: the stick seals zeta(2) = pi^2/6 (Basel) and the functional equation - t", "authority_tier": "engine_derived", "source": "Narrow Highway - a chart: a tick stick placed on the one map", "readable": false, "generated": false}, {"id": "card_alm_connection_zeta_even_powers_are_pi", "title": "Almanac: Inverse even powers fold into pi; inverse odd powers escape into mystery -- the two faces of the zeta function", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Sum the inverse powers of the whole numbers and a startling split appears. For every EVEN power, the sum is a rational number times a power of pi: zeta(2) = 1 + 1/4 + 1/9 + ... = pi^2/6 (t", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_src_mill_tate_1965"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}