Semisemiological structure of the prime numbers and conditional Goldbach theorems.
The main result of this paper implies that if an abelian variety over a field has a maximal isotropic subgroup of -torsion points all of which are defined over , and , then the abelian variety has semistable reduction away from . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its -torsion points are defined over a field and , then the abelian variety has semistable reduction away from . We also give information about the Néron models...
We prove density modulo of the sets of the formwhere is a pair of rationally independent algebraic integers of degree satisfying some additional assumptions, and is any sequence of real numbers.