Brauer groups and Neron Severi groups of surfaces over finite fields

Research Project

Project/Area Number	23K25768
Project/Area Number (Other)	23H01071 (2023)
Research Category	Grant-in-Aid for Scientific Research (B)
Allocation Type	Multi-year Fund (2024) Single-year Grants (2023)
Section	一般
Review Section	Basic Section 11010:Algebra-related
Research Institution	Rikkyo University
Principal Investigator	ガイサトーマス立教大学, 理学部, 教授 (30571963)
Project Period (FY)	2023-04-01 – 2028-03-31
Project Status	Granted (Fiscal Year 2024)
Budget Amount *help	¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000) Fiscal Year 2027: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000) Fiscal Year 2026: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000) Fiscal Year 2025: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000) Fiscal Year 2024: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000) Fiscal Year 2023: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Keywords	ブラウア群 / 有限体 / Brauer group / Neron-Severi group / 有限体上の局面 / Tate-Shafarevich group
Outline of Research at the Start	The first part of the proposal is to apply the a new version of the Artin-Tate formula to calculate Brauer groups and determinants of Neron-Severi groups of special classes of surface. The second part is to find a similar version of the Birch and Swinnerton-Dyer conjecture for abelian surfaces over global fields of characteristic p.