Hilbert's 10th Problem Over Rings of Integers - Ari Shnidman скачать в хорошем качестве

Hilbert's 10th Problem Over Rings of Integers - Ari Shnidman

Joint PU/IAS Number Theory 3:30pm|Simonyi 101 and Remote Access Topic: Hilbert's 10th Problem Over Rings of Integers Speaker: Ari Shnidman Affiliation: The Hebrew University of Jerusalem Date: February 20, 2025 We show that for every quadratic extension of number fields K/F, there exists an abelian variety A/F of positive rank whose rank does not grow upon base change to K. By work of Shlapentokh, this implies that Hilbert's tenth problem over the ring of integers R of any number field has a negative solution. That is, there does not exist an algorithm to determine whether a polynomial equation in several variables over R has solutions in R. This is joint work with Levent Alpöge, Manjul Bhargava, and Wei Ho.