In mathematics, restriction of scalars (also known as "Weil restriction") is a functor which, for any finite extension of fields L/k and any algebraic...

André Weil (/veɪ/; French: [ɑ̃dʁe vɛj]; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic...

scheme Weil distribution Weil divisor Weil group Weil height Weil number Weil pairing Weil–Petersson metric Weil reciprocity law Weil representation Weil restriction...

generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil by David Mumford). Both are derived from the notion...

Restriction of scalars changes S-modules into R-modules. In algebraic geometry, the term "restriction of scalars" is often used as a synonym for Weil...

Group scheme Abelian variety Theta function Grassmannian Flag manifold Weil restriction Differential Galois theory Prime ideal Valuation (algebra) Krull dimension...

this morphism is along a finite extension of fields, it is known as Weil restriction. For any abelian group A, one can form the corresponding diagonalizable...

and restriction relating Hodge A-structures and B-structures for A a subring of B. It was noticed by Jean-Pierre Serre in the 1960s based on the Weil conjectures...

morphism from S {\displaystyle S} to X {\displaystyle X} . Moduli space Weil restriction Rational point Descent along torsors Shafarevich 1994, Ch. VI § 4.1...

is a finite field extension of degree d {\displaystyle d} then the Weil restriction from E {\displaystyle E} to F {\displaystyle F} of the multiplicative...

attaching Galois representations to them. Let S = ResC/R Gm be the Weil restriction of the multiplicative group from complex numbers to real numbers. It...

more abstract terms, the torus T underlying the matrix group is the Weil restriction of the multiplicative group GL(1), from the complex field to the real...

In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be...

In mathematics, the Weil conjecture on Tamagawa numbers is the statement that the Tamagawa number τ ( G ) {\displaystyle \tau (G)} of a simply connected...

product of two projective lines, so by a descent argument X is the Weil restriction to k of the projective line over a quadratic étale algebra K. Since...

These days these are associated to algebraic groups (respectively the Weil restriction from a totally real number field of GL(2), and the symplectic group)...

First, consider the special case where T {\displaystyle T} is the Weil restriction of G m {\displaystyle \mathbb {G} _{\text{m}}} along a finite separable...

34 years on 1 November 2006. Weil held the office for 7 years, up to 2013 state election. Due to legal restrictions, Weil was automatically removed from...

G is any non-trivial connected reductive K-group defined then the Weil restriction H=RK/k(G) is a smooth connected affine k-group for which there is a...

order to prove the Weil conjectures. Étale cohomology theory can be used to construct ℓ-adic cohomology, which is an example of a Weil cohomology theory...

OCLC 1400095204. Weil 1952, p54 Weil 1952, p56 – 59 Weil 1952, p61 Weil 1952, p52 Weil 1952, p66 – 69 Weil 1952, p78 Weil 1952, p82-84 Weil 1952, p87-94 Weil 1952...

In group theory, restriction forms a representation of a subgroup using a known representation of the whole group. Restriction is a fundamental construction...

{\text{res}}_{V}^{U}} are called restriction morphisms. If s ∈ F ( U ) {\displaystyle s\in {\mathcal {F}}(U)} , then its restriction res V U ( s ) {\displaystyle...

Jewry 12. Gefen. p. 12. Weil, Shalva (1997) "Collective Designations and Collective Identity of Ethiopian Jews", in Shalva Weil (ed.) Ethiopian Jews in...

or voting rights compared to Class B or Class C shares. There may be restrictions on any specific issue of class A shares in exchange for the benefits;...

of a left Haar measure was first proven in full generality by André Weil. Weil's proof used the axiom of choice and Henri Cartan furnished a proof that...

symplectic group, first investigated by Irving Segal, David Shale, and André Weil. A natural extension of the representation leads to a semigroup of contraction...

functions. To "classify" addition theorems it is necessary to put some restriction on the type of function G admitted, such that F(x + y) = G(F(x), F(y))...

Universal suffrage would be achieved when all have the right to vote without restriction. It could, for example, look like a system where everyone was presumed...

Howe correspondence), such as the Howe duality conjecture and the Siegel–Weil formula. He has also made contributions to the Gross–Prasad conjecture, the...