Tamagawa Numbers of elliptic curves with C_{13}
... If v does not divide N , then there are no points of order N in E1 (Kv ), as E1 (Kv ) is isomorphic to the formal group of E. If v is also small enough such that there cannot be any points of order N in Ens (kv ), due to the Hasse bound, then it follows that E0 (Kv ) does not have a point of order N ...
... If v does not divide N , then there are no points of order N in E1 (Kv ), as E1 (Kv ) is isomorphic to the formal group of E. If v is also small enough such that there cannot be any points of order N in Ens (kv ), due to the Hasse bound, then it follows that E0 (Kv ) does not have a point of order N ...
2.3 Day 2 Multi-Step Equations
... An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. ...
... An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. ...
Projective p-adic representations of the K-rational geometric fundamental group (with G. Frey).
... A first condition for the existence of such a system {ρ̃Vi } is given by the criterion of Néron-Ogg-Shafarevich: A has to have good reduction everywhere, i.e. at all points of C. A second condition is that the fixed fields of (finite quotients of) the kernels of the ρ̃Vi ’s are regular extensions ...
... A first condition for the existence of such a system {ρ̃Vi } is given by the criterion of Néron-Ogg-Shafarevich: A has to have good reduction everywhere, i.e. at all points of C. A second condition is that the fixed fields of (finite quotients of) the kernels of the ρ̃Vi ’s are regular extensions ...
Very dense subsets of a topological space.
... Proposition (10.4.5). — Given a ring A, the following are equivalent. (a) A is Jacobson. (b) For every non-maximal prime ideal p ⊆ A and every f 6= 0 in B = A/p, Bf is not a field. (b0 ) Every finitely generated A-algebra K which is a field, is finite over A (i.e., finitely generated as an A-module; ...
... Proposition (10.4.5). — Given a ring A, the following are equivalent. (a) A is Jacobson. (b) For every non-maximal prime ideal p ⊆ A and every f 6= 0 in B = A/p, Bf is not a field. (b0 ) Every finitely generated A-algebra K which is a field, is finite over A (i.e., finitely generated as an A-module; ...
ON THE GALOISIAN STRUCTURE OF HEISENBERG
... Galois theory, the different degrees of relative M -indiscernibility defined by the different intermediate fields K ⊆ M ⊆ K p give rise to a lattice of subgroups Gal(K p : K) ⊇ Gal(K p : M ) ⊇ Gal(K p : K p ) of the corresponding Galois group Gal(K p : K). In quantum mechanics, the indeterminacies o ...
... Galois theory, the different degrees of relative M -indiscernibility defined by the different intermediate fields K ⊆ M ⊆ K p give rise to a lattice of subgroups Gal(K p : K) ⊇ Gal(K p : M ) ⊇ Gal(K p : K p ) of the corresponding Galois group Gal(K p : K). In quantum mechanics, the indeterminacies o ...
Rationality and the Tangent Function
... and the solution of the 36 − 54 − 90 triangle. Section 6 also discusses the expression of the numbers tan kπ/n by real radical, which numbers tan kπ/n are algebraic integers, and presents some open problems. Section 7 proves a technical result (Lemma 6) used in Section 5. Properties of the circular ...
... and the solution of the 36 − 54 − 90 triangle. Section 6 also discusses the expression of the numbers tan kπ/n by real radical, which numbers tan kπ/n are algebraic integers, and presents some open problems. Section 7 proves a technical result (Lemma 6) used in Section 5. Properties of the circular ...
Chapter 10. Abstract algebra
... Groups and subgroups are algebraic structures. They are the ones that allow solving equations like x +x =a ⇒x = ...
... Groups and subgroups are algebraic structures. They are the ones that allow solving equations like x +x =a ⇒x = ...
GENERALIZED CAYLEY`S Ω-PROCESS 1. Introduction We assume
... We assume throughout that the base field k is algebraically closed of characteristic zero and that all the geometric and algebraic objetcs are defined over k. A linear algebraic monoid is an affine normal algebraic variety M with an associative product M × M → M which is a morphism of algebraic k–va ...
... We assume throughout that the base field k is algebraically closed of characteristic zero and that all the geometric and algebraic objetcs are defined over k. A linear algebraic monoid is an affine normal algebraic variety M with an associative product M × M → M which is a morphism of algebraic k–va ...