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- ...an Varieties and Moduli|url=https://www.math.purdue.edu/~arapura/preprints/abelian.pdf|archive-url=|archive-date=|access-date=|website=}}</ref> By adding ev === Principally polarized Abelian varieties === ...5 KB (824 words) - 17:32, 19 February 2025
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- ...an Varieties and Moduli|url=https://www.math.purdue.edu/~arapura/preprints/abelian.pdf|archive-url=|archive-date=|access-date=|website=}}</ref> By adding ev === Principally polarized Abelian varieties === ...5 KB (824 words) - 17:32, 19 February 2025
- ...tics, the '''Suslin homology''' is a homology theory attached to algebraic varieties. It was proposed by Suslin in 1987, and developed by {{harvs|txt|last1=Susl By definition, given an abelian group ''A'' and a scheme ''X'' of finite type over a field ''k'', the theor ...1 KB (214 words) - 02:19, 15 April 2020
- ...ink=Igor Shafarevich|first=Igor|year=1961}} proved the formula for abelian varieties with tame ramification over curves, and {{harvs|txt|last=Grothendieck|first ...gg | first=Andrew P. | author-link=Andrew Ogg| title=Cohomology of abelian varieties over function fields | jstor=1970272 | mr=0155824 | year=1962 | journal=[[ ...3 KB (336 words) - 03:05, 14 January 2021
- ...|series=Second Series | year=1989 | title=Multiplicity estimates on group varieties | volume=129 | number=3 | pages=471–500 | doi=10.2307/1971514 | jstor=19715 If <math>G</math> is a [[Abelian group|commutative]] [[algebraic group]] defined over an [[algebraic number ...4 KB (485 words) - 01:39, 16 November 2022
- ...ics)|ramification]] in the field generated by the [[Division point#Abelian varieties|torsion points]]. For an [[abelian variety]] ''A'' defined over a field ''F'' as above, with ring of integers ...4 KB (640 words) - 18:56, 7 July 2020
- ...a [[smooth scheme|smooth]] [[algebraic group]]s) are extensions of Abelian varieties by [[algebraic torus|tori]].<ref>Grothendieck (1972), Théorème 3.6, p. 351< ...so that also the fibres over the <math>s</math> are close to being Abelian varieties. ...4 KB (614 words) - 16:51, 16 February 2024
- ...ov theory]]. A further generalization to general [[abelian variety|abelian varieties]] was also proved by Zhang in 1998. ...|last=Zhang|first=S.-W. |title=Equidistribution of small points on abelian varieties |journal=[[Annals of Mathematics]] |volume=147 |issue=1 |year=1998 |pages=1 ...3 KB (471 words) - 16:46, 4 January 2025
- {{Short description|On heights of points on algebraic varieties over number fields}} ...a|authorlink=Paul Vojta|year=1987}} about heights of points on [[algebraic varieties]] over [[number field]]s. The conjecture was motivated by an analogy betwee ...4 KB (604 words) - 06:27, 13 December 2024
- {{short description|Describes the line bundles on a complex torus or complex abelian variety}} ...orem''' describes the [[line bundle]]s on a [[complex torus]] or complex [[abelian variety]]. ...5 KB (786 words) - 09:06, 21 August 2024
- ...f curves, but not for theta functions of general [[abelian variety|abelian varieties]]. ...ston, MA | isbn=978-0-12-044850-0 | mr=0379510 | year=1974 | chapter=Prym varieties. I | pages=325–350}} ...3 KB (481 words) - 22:08, 14 September 2024
- ...Rosati]], is an involution of the rational [[endomorphism ring]] of an [[abelian variety]] induced by a [[Abelian_variety#Polarisations|polarisation]]. ...lian variety]], let <math>\hat{A} = \mathrm{Pic}^0(A)</math> be the [[dual abelian variety]], and for <math>a\in A</math>, let <math>T_a:A\to A</math> be the ...2 KB (413 words) - 00:34, 29 September 2023
- ...e group of K-rational points of an abelian variety is a finitely-generated abelian group}} ...tional theorem of [[Diophantine geometry]] and the [[arithmetic of abelian varieties]]. ...5 KB (779 words) - 19:23, 30 November 2024
- ...rvard University]] under [[Barry Mazur]] ("Division points on semi-Abelian varieties").<ref>{{cite web |url=https://www.math.harvard.edu/graduate/dissertations/ ...Bloch]] (1926) about holomorphic curves in closed subvarieties of Abelian varieties,<ref>{{cite journal | last=McQuillan | first=Michael Liam | title=A new pro ...6 KB (804 words) - 01:41, 13 June 2024
- ...with certain special varieties are accounted for by finitely many special varieties. ...not expected to occur. When <math>\dim X + \dim Y - \dim U < 0</math>, the varieties <math>X</math> and <math>Y</math> are not expected to intersect at all, so ...8 KB (1,178 words) - 03:22, 5 October 2024
- ...es. Uniruled varieties can be considered to be relatively simple among all varieties, although there are many of them. ...J. Math. 127 (2005), 825-835. Theorem 1.1.</ref>) It is not known whether varieties with these properties exist over the algebraic closure of the [[rational nu ...7 KB (936 words) - 09:15, 12 November 2024
- ...e question of the [[Galois representation]] on the [[Tate module]] of an [[abelian variety]] ''A''. Conjecturally, the image of such a Galois representation, A related conjecture on abelian varieties states that the [[period matrix]] of ''A'' over number field has [[transcen ...6 KB (907 words) - 13:06, 8 November 2023
- ...ry]], '''convexity''' is a restrictive technical condition for [[algebraic varieties]] originally introduced to analyze Kontsevich [[moduli space]]s <math>\over ...et/q/9066 |title=ag.algebraic geometry - Is there any rational curve on an Abelian variety?|website=MathOverflow|access-date=2020-02-28}}</ref> ...9 KB (1,353 words) - 21:58, 7 July 2024
- ...ototypes for more complex examples of higher algebraic structures, such as Abelian [[N-group (category theory)|''n''-groups]]. An Abelian 2-group is a groupoid <math>\mathbb{A}</math> (that is, a [[category (mathe ...10 KB (1,505 words) - 22:46, 1 September 2024
- ...eties]] that the Siegel modular group has to principally polarized abelian varieties. It is the group of automorphisms of '''Z'''<sup>2''n''</sup> preserving a ...5 KB (786 words) - 13:28, 20 October 2023
- ...gma: G \to G, \, x \mapsto x^q</math> for the Frobenius, the [[morphism of varieties]] ...G'' is affine. Thus, the theorem also applies to [[abelian variety|abelian varieties]] (e.g., [[elliptic curve]]s.) In fact, this application was Lang's initial ...5 KB (753 words) - 18:06, 3 November 2024