An Abelian variety is
implies severe restrictions on an Abelian variety. Thus, an Abelian
8 KB (1,216 words) - 20:39, 5 March 2012
$#C+1 = 17 : ~/encyclopedia/old_files/data/C023/C.0203650 Comparison theorem (algebraic geometry)
A theorem on the relations between homotopy invariants of schemes of finite type over
2 KB (271 words) - 13:16, 6 April 2023
Khinchin's theorem on the factorization of distributions: Any probability distribution $P$ adm
...tions on the line, in which factorization theorems analogous to Khinchin's theorem are valid.
2 KB (326 words) - 16:26, 9 April 2016
...is denoted by $\mathrm{NS}(X)$. The Néron–Severi theorem asserts that the Abelian group $\mathrm{NS}(X)$ is finitely generated.
...heory of the base (see, for example, [[#References|[1]]]), a proof of this theorem using topological and transcendental tools. The first abstract proof (valid
4 KB (687 words) - 05:47, 15 April 2023
...additive category]] with set of objects $\mathrm{Ob}(C)$ and let $G$ be an Abelian group. A mapping $\phi: \mathrm{Ob}(C) \to G$ is said to be additive if for
...f coherent and locally free sheaves on schemes in proving the Riemann–Roch theorem. See [[K-functor|$K$-functor]] in algebraic geometry. The group $K(C)$ is u
4 KB (701 words) - 06:11, 26 March 2023
''EGZ theorem''
...\{1,\ldots,2m-1\}$ of cardinality $m$ such that $\sum_{i\in I}a_i=0$. This theorem was first shown in [[#References|[a5]]].
10 KB (1,573 words) - 17:25, 28 January 2020
consisting of the principal ideals. The divisor class group is Abelian and is usually denoted by $ C ( A) $.
Nagata's theorem). If $ B $
5 KB (820 words) - 19:36, 5 June 2020
$#C+1 = 187 : ~/encyclopedia/old_files/data/O110/O.1100050 O\AApNan\ANDScott theorem
A reduction theorem for the class of finite primitive permutation groups, distributing them in
11 KB (1,611 words) - 08:03, 6 June 2020
...s a description of all Abelian extensions (finite Galois extensions having Abelian Galois groups) of a field $ K $
In local class field theory, each finite Abelian extension $ L/K $
17 KB (2,620 words) - 07:48, 13 February 2024
...2 : ~/encyclopedia/old_files/data/K055/K.0505920 Krull\ANDRemak\ANDSchmidt theorem
...or a ring. The lattice-theoretical version of the result is known as Ore's theorem (see [[Modular lattice|Modular lattice]]). For a group $ G $
5 KB (786 words) - 22:15, 5 June 2020
There are no entire elliptic functions except the constants (Liouville's theorem).
are integers (a special case of Abel's theorem, see [[Abelian function|Abelian function]]).
9 KB (1,292 words) - 19:08, 20 January 2022
...ediaofmath.org/legacyimages/b/b015/b015310/b01531041.png" /> is a sheaf of
Abelian groups, then for every <img align="absmiddle" border="0" src="https://www.e
...hemes — see [[#References|[2]]] — can also be interpreted as a base-change
theorem); or 3) <img align="absmiddle" border="0" src="https://www.encyclopediaofma
11 KB (1,513 words) - 17:08, 7 February 2011
[[Abelian variety|Abelian variety]] (cf. also
[[Abelian differential|Abelian differential]]). The polarization class
10 KB (1,582 words) - 22:02, 5 March 2012
...belian varieties and behaves as a functor with respect to the morphisms of Abelian varieties preserving the zero point. For the local aspect see [[#References
...ess (1974) (Appendix in Russian translation: Yu.I. Manin; The Mordell–Weil theorem (in Russian)) {{MR|2514037}} {{MR|1083353}} {{MR|0352106}} {{MR|0441983}} {
6 KB (893 words) - 08:43, 1 May 2023
...gory|Topologized category]]) in dimensions 0, 1. A unified approach to non-Abelian cohomology can be based on the following concept. Let $ C ^{0} $,
fixed. Then a non-Abelian cochain complex is a collection $$
12 KB (1,712 words) - 09:30, 20 December 2019
...maximum condition for subgroups is equivalent to the maximum condition for Abelian subgroups [[#References|[4]]]. A similar result was also established for th
...ups and locally nilpotent groups. It was found, in particular, that if all Abelian subgroups of a locally nilpotent torsion-free group (cf. [[Group without to
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...y existence condition. A non-trivial restriction is the Bruck–Ryser–Chowla theorem, see [[Block design|Block design]]. This condition is not sufficient, as th
...method for symmetric designs which combines Abelian difference sets (cf. [[Abelian difference set]]; [[Difference set|Difference set]]; [[Difference set|Diffe
7 KB (1,152 words) - 16:45, 1 July 2020
A nilpotent, in particular an Abelian, Lie group is solvable. If $ F = \{ V _{i} \} $ is a complete [[Flag|fla
An analogue of Lie's theorem on solvable Lie algebras is true for solvable Lie groups: If $ \rho : \
7 KB (1,043 words) - 18:17, 12 December 2019
...between [[topological group]]s and their [[character group]]s. The duality theorem states that if $ G $
is a locally compact Abelian group and if $ X ( G) $
10 KB (1,483 words) - 17:06, 13 June 2020
$#C+1 = 70 : ~/encyclopedia/old_files/data/L058/L.0508000 Lefschetz theorem
Lefschetz' fixed-point theorem, or the Lefschetz–Hopf theorem, is a theorem that makes it possible to express the number of fixed points of a continuou
11 KB (1,584 words) - 11:51, 8 April 2023