theorem).
Other examples of group schemes are Abelian (group) varieties {{Cite|Mu}}.
5 KB (831 words) - 21:59, 5 March 2012
L. Stickelberger proved the following theorem: For $ r \geq 1 $,
Stickelberger's theorem implies that $ S $
7 KB (1,035 words) - 05:58, 19 March 2022
...m_{i+j=n} \binom{m_1}{i} \binom{m_2}{j}$ follows by the binomial expansion theorem from $(X+Y)^{m_1+m_2} = (X+Y)^{m_1} (X+Y)^{m_2}$.
.... A pre-$\lambda$-ring structure on $\Lambda(R)$ defines a homomorphism of Abelian groups $\lambda_t : R \rightarrow \Lambda(R)$, $\lambda_t(x) = \lambda^0(x)
10 KB (1,721 words) - 07:44, 23 March 2016
...operator whose norm does not exceed one) on a Hilbert space (von Neumann's theorem). This result is closely connected with the existence of a unitary power di
.... In the case when $\mathfrak A$ is the group algebra of a locally compact Abelian group, spectral sets are also called sets of harmonic synthesis.
2 KB (295 words) - 15:46, 29 December 2018
===Siegel's theorem on Dirichlet L-functions===
...lass number of a quadratic field of discriminant $-D$, it follows from the theorem that
5 KB (784 words) - 20:40, 18 October 2014
and an Abelian group $ G $.
By adding $ r $-dimensional chains as linear forms one obtains the Abelian group $ C _ {r} ( K, G) $
6 KB (897 words) - 08:54, 25 April 2022
but this is inessential.) Sheaves of Abelian groups, rings and other structures can be defined similarly.
Giraud's little theorem). Categories equivalent to one of the form $ Sh ( C, \tau ) $
8 KB (1,216 words) - 18:08, 14 November 2023
...cohomology theory" (but not the designation) while studying "generalized Abelian integrals" (now called "Eichler integrals" ; see below).
...idered here, a suitable version of the [[Riemann–Roch theorem|Riemann–Roch theorem]] shows that $C ^ { + } ( \Gamma , k , \mathbf{v} )$ has finite dimension o
13 KB (1,993 words) - 07:12, 15 February 2024
In formulation 1), the Lévy–Cramér theorem admits a generalization to the convolution of two signed measures with rest
...mér theorem to random variables in Euclidean spaces and in locally compact Abelian groups.
4 KB (647 words) - 19:21, 24 March 2023
...er of a group|Character of a group]]). Indeed, if $G$ is a locally compact Abelian group, the Fourier–Stieltjes transform of a finite measure $\mu$ on $\hat
...-definite functions on $G$. This definition is still valid when $G$ is not Abelian.
14 KB (2,163 words) - 19:56, 8 February 2024
component of the identity of the Abelian
Abelian variety, the concept of the degree of polarization of a
4 KB (644 words) - 13:06, 17 April 2023
with semi-integer characteristics one can construct meromorphic Abelian functions with $ 2p $
periods. The periods of an arbitrary Abelian function in $ p $
14 KB (1,941 words) - 05:01, 23 February 2022
i) The uniform convergence theorem: for $ f $
ii) The representation theorem: $ f $
6 KB (794 words) - 22:14, 5 June 2020
of étale Abelian sheaves $ F _ {n} $
is an [[Abelian scheme|Abelian scheme]] over $ X $,
6 KB (932 words) - 11:49, 8 April 2023
...Minkowski addition leads to the [[Brunn–Minkowski theorem|Brunn–Minkowski theorem]] and is the basis for the Brunn–Minkowski theory of convex bodies (i.e.,
...s a convexifying effect; this is made precise by the Shapley–Folkman–Starr theorem.
4 KB (596 words) - 15:30, 1 July 2020
cobordism theorem [[#References|[4]]]). Thus, proving the isomorphism $ M _ {0} \approx M _
...ch can be achieved by methods of algebraic topology. For this reason, this theorem is basic in passing from the homotopy classification of simply-connected ma
10 KB (1,458 words) - 07:41, 10 February 2024
By the Dirichlet unit theorem (cf. also [[Dirichlet theorem|Dirichlet theorem]]), the unit group $ U _ {F} $
that are Abelian over $ \mathbf Q $
6 KB (891 words) - 19:08, 26 March 2023
...y other class of fields. For imaginary quadratic fields, the Brauer–Siegel theorem (stating that for algebraic number fields of fixed degree the following asy
...ory of complex multiplication (see {{Cite|CaFr}}) enables one to construct Abelian extensions of imaginary quadratic fields in an explicit form.
5 KB (867 words) - 17:41, 12 November 2023
...x)$ is divisible (without remainder) by $x-c$ (see [[Bezout theorem|Bezout theorem]]). Every polynomial $f(x)$ with real or complex coefficients has at least
...a field $k$ are roots of unity (cf. [[Fermat little theorem|Fermat little theorem]]) and the subgroup itself is cyclic. This is true, in particular, for the
4 KB (680 words) - 13:40, 30 December 2018
...nd has a complement (see [[Krull–Remak–Schmidt theorem|Krull–Remak–Schmidt theorem]]).
...$ is a perfect ring and $G$ is a finite group. The endomorphism ring of an Abelian group $A$ is perfect only when $A$ is the direct sum of a finite group and
3 KB (491 words) - 19:59, 30 October 2016