In mathematics, the Tate curve is a curve defined over the ring of formal power series Z [ [ q ] ] {\displaystyle \mathbb {Z} [[q]]} with integer coefficients...
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Hodge–Tate theory, which has blossomed into another central technique of modern algebraic number theory. Other innovations of his include the "Tate curve"...
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mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves Ep obtained from an elliptic curve E over the rational...
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recognition of its importance. Tate curve The Tate curve is a particular elliptic curve over the p-adic numbers introduced by John Tate to study bad reduction...
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the results of Tate. Poonen and Stoll gave some examples where the order is twice a square, such as the Jacobian of a certain genus 2 curve over the rationals...
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Tate Buckley Donovan (born September 25, 1963) is an American actor, comedian and television director. He is known for portraying Tom Shayes in Damages...
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mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over...
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and the etale theta theory for line bundles over tempered covers of the Tate curve. On August 30, 2012, Mochizuki released four preprints, whose total size...
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In mathematics, the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve E {\displaystyle E} defined over the field of rational...
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The Altoona Curve are a Minor League Baseball team based in Altoona, Pennsylvania, named after nearby Horseshoe Curve (but also alluding to the curveball...
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Ribet's theorem (redirect from Frey elliptic curve)
the irreducibility and ramification of ρE, p. Using the theory of the Tate curve, one can prove that ρE, p is unramified at q ≠ p and finite flat at q...
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Reuleaux triangle Ribaucour curve[3][4] Riemann–Hurwitz formula Riemann–Roch theorem Riemann surface Road curve Sato–Tate conjecture secant Singular solution...
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primitives based on bilinear mappings on various elliptic curve groups, such as the Weil and Tate pairings, have been introduced. Schemes based on these...
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mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective...
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the quantities on the right-hand side are invariants of the curve, studied by Cassels, Tate, Shafarevich and others (Wiles 2006): # E t o r {\displaystyle...
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elliptic curve, the Néron–Severi group is of rank one and has a unique ample generator, so this generator is often used to define the Néron–Tate height...
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Diophantine equations, and when generalized to hyperelliptic curves, the study of the Sato–Tate conjecture. First assume K {\displaystyle K} is a field of...
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curve over a finite field. Suppose that the generic fiber F of f, which is a curve over the function field k(C), is smooth over k(C). Then the Tate conjecture...
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over a local field, which can be computed using Tate's algorithm. The conductor of an elliptic curve over a local field was implicitly studied (but not...
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. The description of the Tate module for the function field of a curve over a finite field suggests a definition for a Tate module of an algebraic number...
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Anish Kapoor (redirect from C-Curve (sculpture))
the Turner Prize in 1991, the Unilever Commission for the Turbine Hall at Tate Modern, the Padma Bhushan by the Indian government in 2012, a knighthood...
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mathematics, the Edwards curves are a family of elliptic curves studied by Harold Edwards in 2007. The concept of elliptic curves over finite fields is widely...
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Arithmetic of abelian varieties (redirect from Arithmetic of elliptic curve)
elliptic curve. The question of the rank is thought to be bound up with L-functions (see below). The torsor theory here leads to the Selmer group and Tate–Shafarevich...
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Semistable abelian variety (redirect from Semistable elliptic curve)
elliptic curve may be described more concretely as an elliptic curve that has bad reduction only of multiplicative type. Suppose E is an elliptic curve defined...
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Dangerous Curves is a 1988 American comedy film directed by David Lewis and starring Tate Donovan and Grant Heslov. The movie also featured brief appearances...
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Jacobian variety (redirect from Jacobian of a curve)
technique for computing the Jacobian of a curve Hodge structure – these are generalizations of Jacobians Honda–Tate theorem – classifies abelian varieties...
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In mathematics, Tate pairing is any of several closely related bilinear pairings involving elliptic curves or abelian varieties, usually over local or...
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elliptic curves with extra endomorphisms are used to give abelian extensions of global fields. Let Zp be the ring of p-adic integers. The Lubin–Tate formal...
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107. Weisstein, Eric W. "Mordell Curve". MathWorld. Louis Mordell (1969). Diophantine Equations. Silverman, Joseph; Tate, John (1992). "Introduction". Rational...
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proposed by André Weil in 1949 and proved by André Weil in the case of curves. Sato–Tate conjecture Schoof's algorithm Weil's bound Artin, Emil (1924), "Quadratische...
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