The Brauer-Manin-Scharaschkin obstruction for subvarieties of a semi-abelian variety and its dynamical analog

We generalize a result by Stoll on the Brauer-Manin-Scharaschkin obstruction for zero-dimensional subvarieties of abelian varieties to almost split semi-abelian varieties. As consequences, we give an essentially different proof of a partial result on some exponential local-global principle over number fields, originally established by Bartolome, Bilu, and Luca, and generalize it to any global field; we also extend our consideration of this obstruction to a broader situation which has some dynamical interpretation, and improve a result by Hsia and Silverman.