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Examples of abelian surfaces with non-square Tate-Shafarevich group
Examples of abelian surfaces non-square Tate-Shafarevich group Number Theory
2012/6/30
In this article we show the existence of abelian surfaces over Q with Tate-Shafarevich groups having orders five times a square and seven times a square. To obtain this result, we explore the invarian...
The Group of Primitive Almost Pythagorean Triples
Almost pythagorean triples Infinitely generated commutative groups Number Theory
2011/9/6
Abstract: We consider the triples of integer numbers that are solutions of the equation $x^2+qy^2=z^2$, where $q$ is a fixed, square-free arbitrary positive integer. The set of equivalence classes of ...
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...
In a remarkable variety of contexts appears the modular data associated to finite groups. And yet, compared to the well-understood affine algebra modular data, the general properties of this finite g...