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...

enjoyed by all other affine varieties (see Serre's theorem on affineness). But also all of the étale cohomology groups on affine space are trivial. In...

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...

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

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...

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

Serre's theorem in group cohomology Serre's theorem on affineness Serre twist sheaf Serre's vanishing theorem Serre weights Thin set in the sense of Serre Serre...

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 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...

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

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...

particular, Serre's GAGA theorem says that every projective analytic variety is actually an algebraic variety, and the study of holomorphic data on an analytic...

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

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...

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...

Jouanolou's trick is a theorem that asserts, for an algebraic variety X, the existence of a surjection with affine space fibers from an affine variety W to X...

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

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...

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...

There also is Brauer's theorem on induced characters. In mathematics, Brauer's theorem, named for Richard Brauer, is a result on the representability of...

varieties. Serre formulated the Riemann–Roch theorem as a problem of dimension of coherent sheaf cohomology, and also Serre proved Serre duality. Cartan...

of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained...

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...

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...

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

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

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...

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"...