Time: September 10, 2024, 2:00 pm

Place: Room 403, IMI – BAS

Speaker: Boaz Moerman (Utrecht University)

Title: Generalized integral points and strong approximation

Further information: https://icms.bg/generalized-integral-points-and-strong-approximation-talk-by-boaz-moerman/

Abstract. The Chinese remainder theorem states that given coprime integers $p_1, …, p_n$ and integers $a_1, …, a_n$, we can always find an integer $m$ such that $m \equiv a_i \mbox{ mod } p_i$ for all $i$. Similarly given distinct numbers $x_1,…, x_n$ and $y_1, …, y_n$ we can find a polynomial $f$ such that $f(x_i)=y_i$. These statements are two instances of strong approximation for the affine line (over the integers $\mathbb{Z}$ and the polynomials $k[x]$ over a field $k$). In this talk we will consider when an analogue of this holds for special subsets of $\mathbb{Z}$ and $k[x]$, such as squarefree integers or polynomials without simple roots, and different varieties. We give a precise description for which subsets this holds on a toric variety.