W. M. Ruppert

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math.NT1998

Reducibility of polynomials $f (x, y)$ modulo $p$

Wolfgang M. Ruppert

We consider absolutely irreducible polynomials $f \in Z [x, y]$ with $°_{x} (f) = m$ , $°_{y} (f) = n$ and height $H$ . We show that for any prime $p$ with $p > c_{mn} H^{2 mn + n - 1}$ the reduction $…

math.NT1998

Torsion points of abelian varieties in abelian extensions

Wolfgang M. Ruppert

Let A be an abelian variety defined over a number field K and let Kab be the maximal abelian extension of K. We show that there only finitely many torsion points of A which are def…

Reducibility of polynomials f(x,y) modulo p

Torsion points of abelian varieties in abelian extensions

Reducibility of polynomials $f (x, y)$ modulo $p$