搜索结果: 1-9 共查到“数学 OVER NUMBER FIELDS”相关记录9条 . 查询时间(0.158 秒)
ESSENTIAL DIMENSION OF ABELIAN VARIETIES OVER NUMBER FIELDS
ESSENTIAL DIMENSION OVER NUMBER FIELDS
2015/9/29
We affirmatively answer a conjecture in the preprint “Essential
dimension and algebraic stacks,” proving that the essential dimension of an
abelian variety over a number field is inʂ...
On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields
Elliptic Curves over Number Fields Mordell-Weil Group Two-Descent
2013/1/30
We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data inc...
Counting rational points over number fields on a singular cubic surface
rational points over number fields singular cubic surface Number Theory
2012/4/18
A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successful...
On the Surjectivity of Galois Representations Associated to Elliptic Curves over Number Fields
Surjectivity Galois Representations Elliptic Curves over Number Fields Number Theory
2012/4/17
Given an elliptic curve $E$ over a number field $K$, the $\ell$-torsion points $E[\ell]$ of $E$ define a Galois representation $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$. A famous theorem of Serre states t...
Arithmetic of 0-cycles on varieties defined over number fields
zero-cycles Hasse principle weak approximation Brauer-Manin obstruction rationally connected varieties homogeneous spaces
2011/8/30
Abstract: Let $X$ be a rationally connected algebraic variety, defined over a number field $k$. We find a relation between the arithmetic of rational points on $X$ and the arithmetic of zero-cycles. M...
Upper Bounds for the Number of Number Fields with Alternating Galois Group
Number Fields Alternating Galois Group Number Theory
2011/8/26
Abstract: We study the number $N(n, A_n, X)$ of number fields of degree $n$ whose Galois closure has Galois group $A_n$ and whose discriminant is bounded by $X$. By a conjecture of Malle, we expect th...
Hilbert's Tenth Problem and Mazur's Conjectures in Complementary Subrings of Number Fields
Hilbert’s Tenth Problem undecidability elliptic curves primitive divisor
2011/2/24
We show that Hilbert’s Tenth Problem is undecidable for complementary subrings of number fields and that the p-adic and archimedean ring versions of Mazur’s conjectures do not hold in these rings .
Let Q(α) and Q(β) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, Q(β) → Q(α). The algorithm is particularly efficient if the number of isomorphisms is o...
Exact Covering Systems in Number Fields
Exact covering systems Lattice parallelotopes Chinese Remainder Theorem
2011/2/22
It is well known that in an exact covering system in Z, the biggest modulus must be repeated. Very recently, S. Kim proved an analogous result for certain quadratic fields. In this paper, we prove tha...