Hasse principle for intersections of two quadrics via Kummer surfaces

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• Adam Morgan (Cambridge)
• Tuesday 05 November 2024, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jef Laga.

I will discuss recent work with Skorobogatov in which we establish the Hasse principle for a broad class of degree 4 del Pezzo surfaces (including all those with irreducible characteristic polynomial), conditional on finiteness of relevant Tate—Shafarevich groups. A corollary of this work is that the Hasse principle holds for smooth complete intersections of two quadrics in P^n for n\geq 5, conditional on the same conjecture. The proof involves the study of the Hasse principle and Brauer—Manin obstruction on auxiliary Kummer surfaces.

This talk is part of the Number Theory Seminar series.

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