These are the things named after Jean-Pierre Serre, a French mathematician. *

Bass–Serre theory Bass–Serre theory is a part of the Mathematics, mathematical subject of group theory that deals with analyzing the algebraic structure of Group (math), groups Group action (mathematics), acting by automorphisms on simplicial Tree (graph theory), t ...

* Serre class *

Quillen–Suslin theorem The Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra concerning the relationship between free modules and projective modules over polynomial rings. In the geometric setting it is ...

(sometimes known as "Serre's Conjecture" or "Serre's problem") * Serre's Conjecture concerning Galois representations * Serre's "Conjecture II" concerning

linear algebraic group In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation M^TM = I_n wh ...

s * Serre's criterion (there are several of them.) *

Serre duality In algebraic geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre. The basic version applies to vector bundles on a smooth projective variety, but Alexa ...

* Serre–Grothendieck–Verdier duality * Serre's FAC * Serre fibration * Serre's C-theory *

Serre's inequality on height In algebra, specifically in the theory of commutative rings, Serre's inequality on height states: given a (Noetherian) regular ring ''A'' and a pair of prime ideals \mathfrak, \mathfrak in it, for each prime ideal \mathfrak r that is a minimal pri ...

Serre group In mathematics, the Serre group ''S'' is the pro-algebraic group whose representations correspond to CM-motives over the algebraic closure of the rationals, or to polarizable rational Hodge structures with abelian Mumford–Tate groups. It is a pr ...

* Serre's modularity conjecture *

Serre's multiplicity conjectures In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry. Since André Weil's initial definition of intersection n ...

* Serre's open image theorem *

Serre's property FA In mathematics, Property FA is a property of groups first defined by Jean-Pierre Serre. A group ''G'' is said to have property FA if every action of ''G'' on a tree has a global fixed point. Serre shows that if a group has property FA, then it c ...

Serre relations In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any non-zero proper ideals). Throughout the article, unless otherwise stated, a Lie algebra is ...

Serre subcategory In mathematics, Serre and localizing subcategories form important classes of subcategories of an abelian category. Localizing subcategories are certain Serre subcategories. They are strongly linked to the notion of a quotient category. Serre subc ...

Serre functor 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 d ...

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 ...

* Lyndon–Hochschild–Serre spectral sequence * Serre–Swan theorem *

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, ...

* Serre's theorem in group cohomology * Serre's theorem on affineness * Serre twist sheaf *

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 exist ...

* Thin set in the sense of Serre

Notes

{{reflist Serre

See also

Notes