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Demonstrates Hasse principle for intersections of quadrics in high dimensions, indicating broader implications in algebraic geometry.
We prove new cases of the Hasse principle for Kummer surfaces constructed from 2-coverings of Jacobians of genus 2 curves, assuming finiteness of relevant Tate-Shafarevich groups. Under the same assumption, we deduce the Hasse principle for quartic del Pezzo surfaces with trivial Brauer group and irreducible or completely split characteristic polynomial, hence the Hasse principle for smooth complete intersections of two quadrics in the projective space of dimension at least 5.
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Adam Morgan (2026) studied this question.
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