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...

Hodge–Tate theory, which has blossomed into another central technique of modern algebraic number theory. Other innovations of his include the "Tate curve"...

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...

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...

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...

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...

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...

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...

Reuleaux triangle Ribaucour curve[3][4] Riemann–Hurwitz formula Riemann–Roch theorem Riemann surface Road curve Sato–Tate conjecture secant Singular solution...

The Altoona Curve are a Minor League Baseball team based in Altoona, Pennsylvania, named after nearby Horseshoe Curve (but also alluding to the curveball...

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...

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...

primitives based on bilinear mappings on various elliptic curve groups, such as the Weil and Tate pairings, have been introduced. Schemes based on these...

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...

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...

Diophantine equations, and when generalized to hyperelliptic curves, the study of the Sato–Tate conjecture. First assume K {\displaystyle K} is a field of...

Tate Buckley Donovan (born September 25, 1963) is an American actor, comedian and television director. He is known for portraying Tom Shayes in Damages...

algebraic curve is an algebraic curve that is complete as an algebraic variety. A projective curve, a dimension-one projective variety, is a complete curve. A...

In mathematics, Tate pairing is any of several closely related bilinear pairings involving elliptic curves or abelian varieties, usually over local or...

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...

. 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...

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...

107. Weisstein, Eric W. "Mordell Curve". MathWorld. Louis Mordell (1969). Diophantine Equations. Silverman, Joseph; Tate, John (1992). "Introduction". Rational...

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...

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...

In the theory of elliptic curves, Tate's algorithm takes as input an integral model of an elliptic curve E over Q {\displaystyle \mathbb {Q} } , or more...

technique for computing the Jacobian of a curve Hodge structure – these are generalizations of Jacobians Honda–Tate theorem – classifies abelian varieties...

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...

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...

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...