An Infinitesimal $p$-adic Multiplicative Manin-Mumford Conjecture

13 Dec 2018 Serban Vlad

Our results concern analytic functions on the open unit $p$-adic poly-disc in $\mathbb{C}^n_p$ centered at the multiplicative unit and we prove that such functions only vanish at finitely many $n$-tuples of roots of unity $(\zeta_1-1,\ldots,\zeta_n-1)$ unless they vanish along a translate of the formal multiplicative group. For polynomial functions, this follows from the multiplicative Manin-Mumford conjecture... (read more)

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Categories


  • NUMBER THEORY
  • COMMUTATIVE ALGEBRA
  • ALGEBRAIC GEOMETRY