In algebraic geometry, Zariski's main theorem, proved by Oscar Zariski (1943), is a statement about the structure of birational morphisms stating roughly...

extension of Zariski's main theorem to the case when the morphism of varieties need not be birational. Zariski's connectedness theorem gives a rigorous...

Zariski ring Zariski tangent space Zariski surface Zariski topology Zariski–Riemann surface Zariski space (disambiguation) Zariski's lemma Zariski's main...

Tsen's theorem (algebraic geometry) Weber's theorem (algebraic curves) Zariski's connectedness theorem (algebraic geometry) Zariski's main theorem (algebraic...

and closed graph theorems hold Zariski's main theorem – Theorem of algebraic geometry and commutative algebra "The closed graph theorem in various categories"...

theorem Hartshorne's connectedness theorem Zariski's connectedness theorem, a generalization of Zariski's main theorem This disambiguation page lists mathematics...

Paris, initially on the generalization within scheme theory of Zariski's main theorem. In 1968, he also worked with Jean-Pierre Serre; their work led...

it is analytically normal, which is in some sense a variation of Zariski's main theorem. Nagata (1958, 1962, Appendix A1, example 7) gave an example of...

passage to limit. The theorem is used to deduce some other important theorems: Stein factorization and a version of Zariski's main theorem that says that a...

formalism Theorem of absolute purity Theorem on formal functions Ultrabornological space Weil conjectures Vector bundles on algebraic curves Zariski's main theorem...

{\mathcal {O}}_{X}(-1)} . theorem See Zariski's main theorem, theorem on formal functions, cohomology base change theorem, Category:Theorems in algebraic geometry...

target space of f is a normal variety, then f is biregular. (cf. Zariski's main theorem.) A regular map between complex algebraic varieties is a holomorphic...

and only if it is proper and quasi-finite. A generalized form of Zariski Main Theorem is the following: Suppose Y is quasi-compact and quasi-separated...

singularities of surfaces by itself, Zariski used a more roundabout method: he first proved a local uniformization theorem showing that every valuation of...

V\times \mathbb {P} _{k}^{n}\to V} sends Zariski-closed subsets to Zariski-closed subsets. The main theorem of elimination theory is a corollary and a...

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}...

unibranch points are connected. In EGA, the theorem is obtained as a corollary of Zariski's main theorem. Grothendieck, Alexandre; Dieudonné, Jean (1961)...

(Tarnów Mechanical Works), a Polish defense industry manufacturer Zariski's main theorem in mathematics This disambiguation page lists articles associated...

an analytic object to an algebraic one is a functor. The prototypical theorem relating X {\displaystyle X} and X a n {\displaystyle X^{\mathrm {an} }}...

In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively...

primary ideals and proved the first version of the Lasker–Noether theorem. The main figure responsible for the birth of commutative algebra as a mature...

properties Chevalley's theorem on constructible sets Zariski's main theorem Dualizing complex Nagata's compactification theorem "Lemma 28.5.7 (0BA8)—The...

If D were an open set in the Zariski topology we could glue the sheaves; the content of the Beauville–Laszlo theorem is that, under one technical assumption...

geometry. This work, also introducing a preliminary form of the Nash–Moser theorem, was later recognized by the American Mathematical Society with the Leroy...

main significance of normal spaces lies in the fact that they admit "enough" continuous real-valued functions, as expressed by the following theorems...

on X.) Theorem—The prestack of quasi-coherent sheaves over a base scheme S is a stack with respect to the fpqc topology. The proof uses Zariski descent...

then it is ω {\displaystyle \omega } -stable. More generally, the Main gap theorem implies that if there is an uncountable cardinal λ {\displaystyle \lambda...

variety is a line bundle of a divisor. Chow's theorem can be shown via Serre's GAGA principle. Its main theorem states: Let X be a projective scheme over...

as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations...

almost all elements of X, even if it isn't an ultrafilter. The prime number theorem shows that the number of primes less than or equal to n is asymptotically...