geometry, Serre's theorem on affineness (also called Serre's cohomological characterization of affineness or Serre's criterion on affineness) is a theorem due...

ringed space. A theorem of Serre gives a cohomological characterization of an affine variety; it says an algebraic variety is affine if and only if H...

the mathematical fields of topology and K-theory, the Serre–Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the...

Jean-Pierre Serre, a French mathematician. Bass–Serre theory Serre class Quillen–Suslin theorem (sometimes known as "Serre's Conjecture" or "Serre's problem")...

Scheme (mathematics) Projective scheme Spectrum of a matrix Serre's theorem on affineness Étale spectrum Ziegler spectrum Primitive spectrum Stone duality...

The Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra concerning the relationship between...

sheaves on X to coherent analytic sheaves on the associated analytic space Xan. The key GAGA theorem (by Grothendieck, generalizing Serre's theorem on the...

quasi-coherent sheaves F on a noetherian scheme X), then X is Stein (resp. affine); see (Serre 1956) (resp. (Serre 1957) and (Hartshorne 1977, Theorem III.3.7)). Cousin...

specific definitions can be shown to be special case of Serre's definition. In the case of Bézout's theorem, the general intersection theory can be avoided,...

quasi-coherent A {\displaystyle A} -modules. quasi-affine morphism Serre's theorem on affineness EGA 1971, Ch. I, Théorème 9.1.4. harvnb error: no target:...

them (this is discussed at length in Serre's Lectures on the Mordell-Weil theorem). Let A be a thin set in affine n-space over Q and let N(H) denote the...

dimension. This result may be proven using Serre's theorem on regular local rings. Quillen–Suslin theorem Hilbert series and Hilbert polynomial D. Hilbert...

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...

varieties have been called "varieties in the sense of Serre", since Serre's foundational paper FAC on sheaf cohomology was written for them. They remain...

(mathematics) Representation theorem Universal algebra Classic texts on representation theory include Curtis & Reiner (1962) and Serre (1977). Other excellent...

modules over the ring localized on Serre's subcategory of graded modules of finite length; there is also analogous theorem for coherent sheaves when the...

sheaf cohomology Hirzebruch–Riemann–Roch theorem Grothendieck–Riemann–Roch theorem Coherent duality Dévissage Affine scheme Scheme Éléments de géométrie algébrique...

theory for varieties is older, with roots in Bézout's theorem on curves and elimination theory. On the other hand, the topological theory more quickly reached...

the dual of Serre's twisting sheaf O X ( 1 ) {\displaystyle {\mathcal {O}}_{X}(1)} . O X ( 1 ) {\displaystyle {\mathcal {O}}_{X}(1)} Serre's twisting sheaf...

theorems in Diophantine geometry that are of fundamental importance include: Mordell–Weil theorem Roth's theorem Siegel's theorem Faltings's theorem Serge...

In mathematics, the Ax–Grothendieck theorem is a result about injectivity and surjectivity of polynomials that was proved independently by James Ax and...

{\displaystyle d=\dim A} , the Krull dimension. See also: Serre's inequality on height and Serre's multiplicity conjectures. Regular local rings were originally...

who proved the unmixedness theorem for polynomial rings, and for Irvin Cohen (1946), who proved the unmixedness theorem for formal power series rings...

system. The implication of the axiomatic nature of a root system and Serre's theorem is that one can enumerate all possible root systems; hence, "all possible"...

cohomology. Serre's vanishing theorem states that if X is a projective variety and F a coherent sheaf on it, then, for sufficiently large n, the Serre twist...

1945. Artin & Whaples 1946. Serre 1967, p. 140. Serre 1979, p. 197. Neukirch 1999, p. 391. Neukirch 1999, p. 300, Theorem 6.3. Artin, Emil; Whaples, George...

independently prove the Quillen–Suslin theorem ("Serre's conjecture") about the triviality of algebraic vector bundles on affine space. Fossil footprints of bipedal...

order a prime power. The best general result to date is the Bruck–Ryser theorem of 1949, which states: If n is a positive integer of the form 4k + 1 or...

are results on finite-dimensionality of cohomology, results on the vanishing of cohomology in various cases, duality theorems such as Serre duality, relations...

holomorphic n {\displaystyle n} -forms on V {\displaystyle V} . This is the dualising object for Serre duality on V {\displaystyle V} . It may equally well...