In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the...
33 KB (4,920 words) - 14:54, 23 June 2024
and Doja Cat "The Motive" (song), a 1987 song by Then Jerico Motive (algebraic geometry) Motive, Inc, a software manufacturer Motive Studio, a video game...
1 KB (149 words) - 15:28, 4 July 2024
of general type Zariski surface Algebraic variety Hypersurface Quadric (algebraic geometry) Dimension of an algebraic variety Hilbert's Nullstellensatz...
7 KB (600 words) - 19:55, 10 January 2024
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...
41 KB (5,759 words) - 22:50, 17 June 2024
geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry...
37 KB (4,753 words) - 14:39, 23 July 2024
Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local...
14 KB (1,810 words) - 16:44, 31 July 2024
arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around...
15 KB (1,464 words) - 19:56, 6 May 2024
Pierre Deligne (redirect from Deligne motive)
Logarithmic form Kodaira vanishing theorem Moduli of algebraic curves Motive (algebraic geometry) Perverse sheaf Riemann–Hilbert correspondence Serre's...
19 KB (1,932 words) - 16:47, 12 June 2024
ring of algebraic cycles as a special case. Some of the deepest problems in algebraic geometry and number theory are attempts to understand motivic cohomology...
16 KB (2,285 words) - 19:58, 29 December 2023
In algebraic geometry, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of...
8 KB (974 words) - 03:21, 4 December 2023
reconstructed from the Banach algebra of functions on the space (Gelfand–Naimark). In commutative algebraic geometry, algebraic schemes are locally prime...
21 KB (2,384 words) - 15:46, 26 May 2024
In algebraic geometry, a correspondence between algebraic varieties V and W is a subset R of V×W, that is closed in the Zariski topology. In set theory...
2 KB (293 words) - 16:11, 20 March 2022
Alexander Grothendieck (category Algebraic geometers)
of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory...
77 KB (8,255 words) - 07:11, 29 June 2024
mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology of...
9 KB (1,472 words) - 14:41, 4 January 2022
in Unicode or amsmath LaTeX) is sometimes used by number theorists and algebraic geometers to designate the group scheme of n-th roots of unity. Note:...
33 KB (2,024 words) - 04:10, 1 August 2024
Field with one element (redirect from Non-additive geometry)
abstract properties. This allows the development of commutative algebra and algebraic geometry on new foundations. One of the defining features of theories...
32 KB (3,811 words) - 00:05, 8 July 2024
Chow group (category Algebraic geometry)
In algebraic geometry, the Chow groups (named after Wei-Liang Chow by Claude Chevalley (1958)) of an algebraic variety over any field are algebro-geometric...
26 KB (4,195 words) - 23:25, 28 November 2023
mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories...
11 KB (1,359 words) - 06:15, 3 April 2022
theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory,...
189 KB (19,500 words) - 16:08, 29 July 2024
Motivic integration is a notion in algebraic geometry that was introduced by Maxim Kontsevich in 1995 and was developed by Jan Denef and François Loeser...
2 KB (150 words) - 22:21, 28 April 2021
Kähler differential (redirect from Algebraic de Rham cohomology)
standard in commutative algebra and algebraic geometry somewhat later, once the need was felt to adapt methods from calculus and geometry over the complex numbers...
26 KB (4,378 words) - 08:13, 20 September 2023
mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived categories...
26 KB (4,702 words) - 03:51, 1 July 2024
Chow's moving lemma (category Theorems in algebraic geometry)
Joel (1972). "Chow's moving lemma. Appendix 2 to: "Motives" by Steven L. Kleiman.". Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer School in Math...
1 KB (189 words) - 14:43, 25 July 2024
In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties...
7 KB (577 words) - 10:22, 12 February 2024
of geometry. Fundamentally, it studies algebraic varieties. Algebraic graph theory a branch of graph theory in which methods are taken from algebra and...
72 KB (7,687 words) - 21:49, 25 July 2024
Yuri Manin (category Algebraic geometers)
2023) was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical...
20 KB (1,548 words) - 04:05, 20 July 2024
Dieudonné; The historical development of algebraic geometry Charles Weibel; History of homological algebra Peter Johnstone; The point of pointless topology...
87 KB (273 words) - 01:34, 14 June 2024
study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number...
52 KB (8,365 words) - 15:51, 30 July 2024
Crystalline cohomology (redirect from Algebraic de Rham theorem)
2022-02-08 Illusie, Luc (1975), "Report on crystalline cohomology", Algebraic geometry, Proc. Sympos. Pure Math., vol. 29, Providence, R.I.: Amer. Math....
15 KB (1,922 words) - 09:44, 26 September 2022
Crystal (mathematics) (redirect from Crystal (geometry))
2022-02-08 Illusie, Luc (1975), "Report on crystalline cohomology", Algebraic geometry, Proc. Sympos. Pure Math., vol. 29, Providence, R.I.: Amer. Math....
7 KB (844 words) - 13:50, 22 December 2022