Дата: 10.09.2024 г., 14:00 ч.

Място: Зала 403, ИМИ – БАН

Докладчик: Боаз Моерман (Утрехтски университет)

Доклад: Generalized integral points and strong approximation

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

Резюме. 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.