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...

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...

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}...

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

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

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...

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

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

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...

The modularity theorem (formerly called the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture or modularity conjecture for elliptic curves)...

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...

{\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...

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

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

mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood...

than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself...

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

An important tool for proving the existence of these points is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent...

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...

(dissertation in which he solved Hilbert's 7th problem, German) Schneider–Lang theorem L.-Ch. Kappe, H.P.Schlickewei, Wolfgang Schwarz Theodor Schneider zum...

has only one isomorphism class (since all such bundles are trivial by Lang's theorem). Its group of automorphisms is G m {\displaystyle \mathbb {G} _{m}}...

projective spaces. It was introduced by Faltings (1991) in his proof of Lang's conjecture that subvarieties of an abelian variety containing no translates...

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

for the symmetry to hold are given by Schwarz's theorem, also called Clairaut's theorem or Young's theorem. In the context of partial differential equations...

2b^{9(m+n)}.} In the 1960s Serge Lang proved a result using this non-explicit form of auxiliary functions. The theorem implies both the Hermite–Lindemann...

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