$#A+1 = 52 n = 0
...s (cf. [[Grothendieck category|Grothendieck category]]). Let $ \mathfrak A $
10 KB (1,375 words) - 22:17, 5 June 2020
...in the theory of field extensions (cf. [[Extension of a field|Extension of a field]]). Let $ K $
be some extension of a field $ k $ .
6 KB (793 words) - 17:24, 17 December 2019
...e positive rational number $-r''$: $-r'>-r''$. The absolute value $|r|$ of a rational number $r$ is defined in the usual way: $|r|=r$ if $r\geq0$ and $|
...tional fractions containing the sum and product of two rational fractions $a/b$ and $c/d$ belonging to $r'$ and $r''$, respectively. The order, sum and
6 KB (1,000 words) - 15:36, 14 February 2020
$#A+1 = 43 n = 0
A covariant (or contravariant) functor $ F $
6 KB (837 words) - 07:19, 14 November 2023
''of an $m \times n$-matrix $A = \left\Vert a_{ij} \right\Vert$''
\mathrm{per}(A) = \sum_\sigma a_{1\sigma(1)}\cdots a_{m\sigma(m)}
8 KB (1,228 words) - 19:13, 17 March 2023
...he Narasimhan–Seshadri moduli spaces is still (1998) going on, e.g. on the ring structure of their real cohomology; see, e.g., [[#References|[a6]]] for mor
...|Lie group]] $G$ with an invariant scalar product on its [[Lie algebra|Lie algebra]]. The connections of interest are the so-called instantons, the solutions
7 KB (1,126 words) - 17:45, 1 July 2020
$#A+1 = 27 n = 0
$#C+1 = 27 : ~/encyclopedia/old_files/data/A011/A.0101720 Algebraic varieties, arithmetic of,
5 KB (793 words) - 16:10, 1 April 2020
...theory and in physics. For number theorists, the seminal paper is that of A. Weil, [[#References|[a1]]]. He cites earlier papers of I. Segal and D. Sha
...vial. Extend $\chi$ to $L$ in an arbitrary manner, then induce. This gives a model for $\pi$.
7 KB (1,158 words) - 20:32, 13 March 2024
An ''elliptic curve'' is a non-singular complete
curves is the source of a large part of contemporary algebraic
19 KB (3,251 words) - 20:37, 19 September 2017
$#A+1 = 90 n = 0
$#C+1 = 90 : ~/encyclopedia/old_files/data/A010/A.0100200 Abelian category
10 KB (1,515 words) - 18:19, 31 March 2020
$#A+1 = 43 n = 0
A [[Lattice|lattice]] in which the modular law is valid, i.e. if $ a \leq c $,
6 KB (942 words) - 06:28, 8 June 2024
...convenient to formulate a variety of enumeration or counting questions in a unified way in terms of the concept of an arithmetical semi-group $G$ (cf.
G(n) = \# \{ a \in G : |a| = n \} \ ,
14 KB (2,037 words) - 09:45, 11 November 2023
It is a Laurent polynomial of two variables associated to ambient isotopy classes o
...braid theorem]]), or statistical mechanics (interpreting the polynomial as a state sum, cf. also [[Statistical mechanics, mathematical problems in|Stati
18 KB (2,713 words) - 05:14, 15 February 2024
''[[Linear space]], over a [[field]] $K$''
...ely, in which a multiplication of the elements by scalars is defined, i.e. a [[mapping]]
14 KB (2,558 words) - 11:28, 21 June 2016
A natural generalization of the concept of the [[Picard variety]] $ \mathfr
for a smooth [[algebraic variety]] $ X $
7 KB (1,008 words) - 07:42, 20 March 2024
$#A+1 = 88 n = 0
...l manifold $ M $ (including a generalized manifold) with coefficients in a locally constant system of groups (modules) $ {\mathcal G} $,
8 KB (1,257 words) - 05:06, 7 March 2022
...on $ X $; the set of line bundles with the tensor product operation forms a group $ \operatorname{Pic}(X) \cong {H^{1}}(X,\mathcal{O}_{X}^{*}) $ (cf. [
...ve bundle $ \mathbf{P}(E) $, just like to a vector space one can associate a [[Projective scheme|projective space]].
14 KB (2,169 words) - 08:12, 14 December 2016
$#A+1 = 129 n = 1
An invariant of a homotopy class of mappings of topological spaces. It was first defined by H
12 KB (1,812 words) - 22:11, 5 June 2020
$#A+1 = 127 n = 0
''with values in a sheaf of Abelian groups''
10 KB (1,477 words) - 22:17, 5 June 2020
...sentation of a]]). However, whereas for finite groups the reduction modulo a prime $p$ happens with respect to the field of coefficients of the represen
...ement "decreasing" in the definition above is dropped, $\lambda$ is called a composition of $r$ into $n$ parts. The union of the sets $\Lambda ( n , r )
33 KB (5,081 words) - 10:26, 11 November 2023