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...

Zahorski theorem (real analysis) Zariski's connectedness theorem (algebraic geometry) Zariski's main theorem (algebraic geometry) Zeckendorf's theorem (number...

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

Webbed space – Space where open mapping and closed graph theorems hold Zariski's main theorem – Theorem of algebraic geometry and commutative algebra Rudin...

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...

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...

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...

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

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...

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

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

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}...

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

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

an analytic object to an algebraic one is a functor. The prototypical theorem relating X and Xan says that for any two coherent sheaves F {\displaystyle...

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...

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

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

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

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...

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...

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...

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...

theorems concerning a PID, the most important one is the structure theorem for finitely generated modules over a principal ideal domain. The theorem may...

category C which satisfies any one of the following three properties. (A theorem of Jean Giraud states that the properties below are all equivalent.) There...

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

conjecture called Fermat's Last Theorem is an example of the power of this approach. In classical algebraic geometry, the main objects of interest are the...