Video library: Yu. V. Nesterenko, On solvability of diophantine equations in $p$-adic numbers

VIDEO LIBRARY


International conference "Arithmetic as Geometry: Parshin Fest" November 27, 2012 11:00, Moscow, Steklov Mathematical Institute of RAS

On solvability of diophantine equations in $p$-adic numbers Yu. V. Nesterenko M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract: We will discuss the following phenomenon: if a system of polynomial equations with integral coefficients is solvable modulo $n$-th power of a prime number $p$, and $n$ is an integer larger than some constant effectively dependent on degrees and heights of polynomials forming the system, then this system has a solution in $p$-adic numbers. Language: English