The number of maximal torsion cosets in subvarieties of tori

César Martínez (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We present sharp bounds on the number of maximal torsion cosets in a subvariety of the complex algebraic torus $\Gm^n$. Our first main result gives a bound in terms of the degree of the defining polynomials. A second result gives a bound in terms of the toric degree of the subvariety. As a consequence, we prove the conjectures of Ruppert and of Aliev and Smyth on the number of isolated torsion points of a hypersurface. These conjectures bound this number in terms of the multidegree and the volume of the Newton polytope of a polynomial defining the hypersurface, respectively.

Domaines: Théorie des nombres [math.NT]

César Martínez. The number of maximal torsion cosets in subvarieties of tori. 2015. ⟨hal-01140886v3⟩