Seminar: An infinite family of Del Pezzo surfaces violating the Hasse principle

Thời gian: 13:00 đến 15:00 Ngày 30/05/2025

Địa điểm: Phòng A502, VIASM

Báo cáo viên: Nguyễn Xuân Thọ (Hanoi University of Science and Technology)

Tóm tắt: Using the recent work of S. Y. Xiao [Prime values of fa,b2 and fa,p2,f quadratic, Algebra Number Theory, 18 (9) (2024), 1619-1679], we construct an infinite family of degree 4 del Pezzo surfaces which violates the Hasse principle. This family contains the surface studied by Birch and Swinnterton-Dyer [The Hasse problem for rational surfaces, J. Reine Angew. Math. 274/275 (1975) 164-174] and the family studied by Quan [The arithmetic of certain del Pezzo surfaces and K3 surfaces, J. Théor. Nombres Bordx. 24 (2) (2012) 447-460].