In algebraic geometry, Lang's theorem, introduced by Serge Lang, states: if G is a connected smooth algebraic group over a finite field F q {\displaystyle...

Schneider–Lang theorem is a refinement by Lang (1966) of a theorem of Schneider (1949) about the transcendence of values of meromorphic functions. The theorem implies...

introduced the Lang map, the Katz–Lang finiteness theorem, and the Lang–Steinberg theorem (cf. Lang's theorem) in algebraic groups. Lang was a prolific...

In number theory, the Katz–Lang finiteness theorem, proved by Nick Katz and Serge Lang (1981), states that if X is a smooth geometrically connected scheme...

Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field Q {\displaystyle \mathbb {Q}...

proof of the theorem makes extensive use of methods from mathematical logic, such as model theory. One first proves Serge Lang's theorem, stating that...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

reals, then both Roth's conclusion and Lang's hold for almost all α {\displaystyle \alpha } . So both the theorem and the conjecture assert that a certain...

Bombieri's theorem may refer to: Bombieri–Vinogradov theorem, a result in analytic number theory Schneider–Lang theorem for Bombieri's theorem on transcendental...

Encyclopedia of Mathematics, EMS Press, 2001 [1994] Lang's review of Mordell's Diophantine Equations Mordell's review of Lang's Diophantine Geometry...

groups constructed from simple algebraic groups over finite fields. Lang's theorem Generalized flag variety, Bruhat decomposition, BN pair, Weyl group...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

{\displaystyle \operatorname {Spec} \mathbf {F} _{q}} is trivial. (Lang's theorem.) If P is a parabolic subgroup of a smooth affine group scheme G with...

In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

most 1, H1(k,G) = 1. (The case of a finite field was known earlier, as Lang's theorem.) It follows, for example, that every reductive group over a finite...

In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard...

In number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way...

In real analysis, a branch of mathematics, the inverse function theorem is a theorem that asserts that, if a real function f has a continuous derivative...

In multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does...

Vaseršteĭn later gave a simpler and much shorter proof of the theorem, which can be found in Serge Lang's Algebra. A generalization relating projective modules...

has also grown significantly since its inception in the 1990s with Robert Lang's TreeMaker algorithm to assist in the precise folding of bases. Computational...

In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable...

In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite...

correspondences. The seesaw theorem is proved using proper base change. It can be used to prove the theorem of the cube. Lang (1959, p.241) originally stated...

theorem (proof theory) Deduction theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem...

holomorphic maps from C. Lang conjectured that the analytic and algebraic special sets are equal. Subspace theorem Schmidt's subspace theorem shows that points...

between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group...

In mathematics, Siegel's theorem on integral points states that a curve of genus greater than zero has only finitely many integral points over any given...

shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular...

In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing...