Algebraic Groups.Tori

Topic Algebraic Tori admitted

Definition Algebraic Torus admitted

Definition Anisotropic Torus admitted

Topic Character and Cocharacter Lattices admitted

Theorem Characters Are Group-Like Elements admitted

Theorem Classification of Rank-One Tori admitted

Example Classification of Real Tori admitted

Theorem Convolution Is Pointwise Multiplication admitted

Theorem F-Tori Are Classified by Galois Modules admitted

Theorem Finiteness of Tori of Bounded Rank admitted

Theorem Galois Descent for Hopf Algebras admitted

Theorem Galois Descent for Vector Spaces admitted

Theorem Homomorphisms of Tori Correspond to Lattice Maps admitted

Definition Induced Torus admitted

Example Norm-One Torus of a Separable Extension admitted

Definition Rank and Split Rank of a Torus admitted

Theorem Resolution of a Torus by Induced Tori admitted

Definition Split Torus admitted

Theorem Split-Anisotropic Decomposition of a Torus admitted

Theorem Subtori and Quotients via the Character Lattice admitted

Definition Tamely Ramified Torus admitted

Definition The Diagonalizable Group Scheme D(M) admitted

Theorem The Minimal Splitting Field of a Torus admitted

Definition The Twisted Form of a Galois Lattice admitted

Theorem Tori Are Classified by Cocycles in GL_n(Z) admitted

Theorem Tori among Groups of Multiplicative Type admitted

Example Tori over Finite Fields admitted

Theorem Tori up to Isogeny Are Rational Representations admitted

Definition Unramified Torus admitted

Definition Weakly Induced Torus admitted

Theorem Weil Restriction of Tori admitted