Arithmetic of abelian varieties information

mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back...

Historically the first abelian varieties to be studied were those defined over the field of complex numbers. Such abelian varieties turn out to be exactly...

Arithmetic dynamics Arithmetic of abelian varieties Birch and Swinnerton-Dyer conjecture Moduli of algebraic curves Siegel modular variety Siegel's theorem...

arithmetic geometry that explicitly includes the 'infinite primes'. Arithmetic of abelian varieties See main article arithmetic of abelian varieties Artin...

of Mathematical Sciences. Vol. 49 (Second ed.). ISBN 978-3-540-20364-3. ISSN 0938-0396. Zbl 1079.11002. Arithmetic Chow groups Arithmetic of abelian varieties...

number Arithmetic of abelian varieties Elliptic divisibility sequences Mordell curve Fermat's Last Theorem Mordell conjecture Euler's sum of powers conjecture...

call the book "visionary". A larger field sometimes called arithmetic of abelian varieties now includes Diophantine geometry along with class field theory...

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements...

reductions of semi-stable varieties", Compositio Mathematica, 104 (1): 77–105. Zhang, Shou-Wu (1998), "Equidistribution of small points on abelian varieties",...

dynamics, the study of the iteration of self-maps of the complex plane or other complex algebraic varieties. Arithmetic dynamics is the study of the number-theoretic...

Rosati involution), leading to a classification of CM-type abelian varieties. To construct such varieties in the same style as for elliptic curves, starting...

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus...

This is a timeline of the theory of abelian varieties in algebraic geometry, including elliptic curves. c. 1000 Al-Karaji writes on congruent numbers Fermat...

Another class is formed by the abelian varieties, which are the algebraic groups whose underlying variety is a projective variety. Chevalley's structure theorem...

Abelian varieties are a natural generalization of elliptic curves, including algebraic tori in higher dimensions. Just as elliptic curves have a natural...

{A}}_{g}} of principally polarized complex abelian varieties of dimension g {\displaystyle g} (a principal polarization identifies an abelian variety with...

asks which principally polarized abelian varieties are the Jacobians of curves. The Picard variety, the Albanese variety, generalized Jacobian, and intermediate...

On the other hand, an abelian scheme may not be projective. Examples of abelian varieties are elliptic curves, Jacobian varieties and K3 surfaces. Let...

of abelian varieties. The Selmer group of an abelian variety A with respect to an isogeny f : A → B of abelian varieties can be defined in terms of Galois...

variety ResL/kX, defined over k. It is useful for reducing questions about varieties over large fields to questions about more complicated varieties over...

In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same...

He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Taniyama–Shimura conjecture...

(or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions...

answer questions of arithmetic significance. The category of group schemes is somewhat better behaved than that of group varieties, since all homomorphisms...