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List Of Things Named After Jean-Pierre Serre
These are the things named after Jean-Pierre Serre, a French mathematician. *Bass–Serre theory *Serre class *Quillen–Suslin theorem (sometimes known as "Serre's Conjecture" or "Serre's problem") *Serre conjecture (number theory), Serre's Conjecture concerning Galois representations *Serre's conjecture II (algebra), Serre's "Conjecture II" concerning linear algebraic groups *Serre's criterion (there are several of them.) *Serre duality *Coherent duality, Serre–Grothendieck–Verdier duality *List_of_important_publications_in_mathematics#Faisceaux_Alg%C3%A9briques_Coh%C3%A9rents, Serre's FAC *Serre fibration *Localization_of_a_category#Serre's_C-theory, Serre's C-theory *Serre's inequality on height *Serre group *Serre's modularity conjecture *Serre's multiplicity conjectures *Serre's open image theorem *Serre's property FA *Serre relations *Serre subcategory *Serre functor *Serre spectral sequence *Lyndon–Hochschild–Serre spectral sequence *Serre–Swan theorem *Serre–Tate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Pierre Serre
Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003. Biography Personal life Born in Bages, Pyrénées-Orientales, France, to pharmacist parents, Serre was educated at the Lycée de Nîmes and then from 1945 to 1948 at the École Normale Supérieure in Paris. He was awarded his doctorate from the Sorbonne in 1951. From 1948 to 1954 he held positions at the Centre National de la Recherche Scientifique in Paris. In 1956 he was elected professor at the Collège de France, a position he held until his retirement in 1994. His wife, Professor Josiane Heulot-Serre, was a chemist; she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, historian and writer Claudine Monteil. The French mathematician Denis S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thin Set (Serre)
In mathematics, a thin set in the sense of Serre, named after Jean-Pierre Serre, is a certain kind of subset constructed in algebraic geometry over a given field ''K'', by allowed operations that are in a definite sense 'unlikely'. The two fundamental ones are: solving a polynomial equation that may or may not be the case; solving within ''K'' a polynomial that does not always factorise. One is also allowed to take finite unions. Formulation More precisely, let ''V'' be an algebraic variety over ''K'' (assumptions here are: ''V'' is an irreducible set, a quasi-projective variety, and ''K'' has characteristic zero). A type I thin set is a subset of ''V''(''K'') that is not Zariski-dense. That means it lies in an algebraic set that is a finite union of algebraic varieties of dimension lower than ''d'', the dimension of ''V''. A type II thin set is an image of an algebraic morphism (essentially a polynomial mapping) φ, applied to the ''K''-points of some other ''d''-dimensional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serre's Vanishing Theorem
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties. Many geometric questions can be formulated as questions about the existence of sections of line bundles or of more general coherent sheaves; such sections can be viewed as generalized functions. Cohomology provides computable tools for producing sections, or explaining why they do not exist. It also provides invariants to distinguish one algebraic variety from another. Much of algebraic geometry and complex analytic geometry is formulated in terms of coherent sheaves and their cohomology. Coherent sheaves Coherent sheaves can be seen as a generalization of vector bundles. There is a notion of a coherent analytic sheaf on a complex analytic space, and an analogous notion of a coherent algebraic sheaf on a scheme. In both cases, the given space X comes with a sheaf of rings \mathcal O_X, the sheaf of holomor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serre Twist Sheaf
In algebraic geometry, Proj is a construction analogous to the spectrum-of-a-ring construction of affine schemes, which produces objects with the typical properties of projective spaces and projective varieties. The construction, while not functorial, is a fundamental tool in scheme theory. In this article, all rings will be assumed to be commutative and with identity. Proj of a graded ring Proj as a set Let S be a graded ring, whereS = \bigoplus_ S_iis the direct sum decomposition associated with the gradation. The irrelevant ideal of S is the ideal of elements of positive degreeS_+ = \bigoplus_ S_i .We say an ideal is homogeneous if it is generated by homogeneous elements. Then, as a set,\operatorname S = \. For brevity we will sometimes write X for \operatorname S. Proj as a topological space We may define a topology, called the Zariski topology, on \operatorname S by defining the closed sets to be those of the form :V(a) = \, where a is a homogeneous ideal of S. As in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serre's Theorem On Affineness
In the mathematical discipline of algebraic geometry, Serre's theorem on affineness (also called Serre's cohomological characterization of affineness or Serre's criterion on affineness) is a theorem due to Jean-Pierre Serre which gives sufficient conditions for a scheme to be affine. The theorem was first published by Serre in 1957. Statement Let be a scheme with structure sheaf If: :(1) is quasi-compact, and :(2) for every quasi-coherent ideal sheaf of -modules, , then is affine. Related results * A special case of this theorem arises when is an algebraic variety, in which case the conditions of the theorem imply that is an affine variety In algebraic geometry, an affine variety, or affine algebraic variety, over an algebraically closed field is the zero-locus in the affine space of some finite family of polynomials of variables with coefficients in that generate a prime idea .... * A similar result has stricter conditions on but looser conditions on the cohomology: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serre–Tate Theorem
In algebraic geometry, the Serre–Tate theorem says that an abelian scheme and its p-divisible group have the same infinitesimal deformation theory. This was first proved by Jean-Pierre Serre when the reduction of the abelian variety is ordinary, using the Greenberg functor; then John Tate gave a proof in the general case by a different method. Their proofs were not published, but they were summarized in the notes of the Lubin–Serre–Tate seminar (Woods Hole, 1964). Other proofs were published by Messing (1962) and Drinfeld Vladimir Gershonovich Drinfeld ( uk, Володи́мир Ге́ршонович Дрінфельд; russian: Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a renowne ... (1976). References * : see, vol.2, p. 854, comments on Tate's letter from Jan.10, 1964. * Abelian varieties Theorems in algebraic geometry {{Abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serre–Swan Theorem
In 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 algebraic concept of projective modules and gives rise to a common intuition throughout mathematics: "projective modules over commutative rings are like vector bundles on compact spaces". The two precise formulations of the theorems differ somewhat. The original theorem, as stated by Jean-Pierre Serre in 1955, is more algebraic in nature, and concerns vector bundles on an algebraic variety over an algebraically closed field (of any characteristic). The complementary variant stated by Richard Swan in 1962 is more analytic, and concerns (real, complex, or quaternionic) vector bundles on a smooth manifold or Hausdorff space. Differential geometry Suppose ''M'' is a smooth manifold (not necessarily compact), and ''E'' is a smooth vector bundle over ''M''. Then ''Γ(E)'', the space of smooth sections of ''E'', is a module o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyndon–Hochschild–Serre Spectral Sequence
In mathematics, especially in the fields of group cohomology, homological algebra and number theory, the Lyndon spectral sequence or Hochschild–Serre spectral sequence is a spectral sequence relating the group cohomology of a normal subgroup ''N'' and the quotient group ''G''/''N'' to the cohomology of the total group ''G''. The spectral sequence is named after Roger Lyndon, Gerhard Hochschild, and Jean-Pierre Serre. Statement Let G be a group and N be a normal subgroup. The latter ensures that the quotient G/N is a group, as well. Finally, let A be a G-module. Then there is a spectral sequence of cohomological type :H^p(G/N,H^q(N,A)) \Longrightarrow H^(G,A) and there is a spectral sequence of homological type :H_p(G/N,H_q(N,A)) \Longrightarrow H_(G,A), where the arrow '\Longrightarrow' means convergence of spectral sequences. The same statement holds if G is a profinite group, N is a ''closed'' normal subgroup and H^* denotes the continuous cohomology. Examples Homo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serre Spectral Sequence
In mathematics, the Serre spectral sequence (sometimes Leray–Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an important tool in algebraic topology. It expresses, in the language of homological algebra, the singular (co)homology of the total space ''X'' of a (Serre) fibration in terms of the (co)homology of the base space ''B'' and the fiber ''F''. The result is due to Jean-Pierre Serre in his doctoral dissertation. Cohomology spectral sequence Let f\colon X\to B be a Serre fibration of topological spaces, and let ''F'' be the (path-connected) fiber. The Serre cohomology spectral sequence is the following: : E_2^ = H^p(B, H^q(F)) \Rightarrow H^(X). Here, at least under standard simplifying conditions, the coefficient group in the E_2-term is the ''q''-th integral cohomology group of ''F'', and the outer group is the singular cohomology of ''B'' with coefficients in that group. Strictly speaking, what is meant is cohomology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serre Functor
{{Disambiguation, geo ...
Serre may refer to: * Serre (surname) * Serre (grape), a red Italian wine grape * Serre (river), a tributary of the Oise in France * Serre, Campania, a town and comune in Salerno, Campania, Italy * Serre-lès-Puisieux, a village in Pas-de-Calais department, northern France * Serre Chevalier, a French ski resort in the Alps * Serre Calabresi, a mountain and hill area of Calabria, Italy See also * Serr, a surname * Serres (other) * La Serre (other) La Serre might refer to: * Jean Puget de la Serre (1594-1665), writer and dramatist * Jean-Louis-Ignace de La Serre (1662-1757), writer and dramatist * Charles Barbier de la Serre (1767-1841), cryptographer * La Serre, commune in the department ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
