On the Hasse Principle for Systems of Forms

NORTHEY, MATTHEW JOSEPH (2022) On the Hasse Principle for Systems of Forms. Doctoral thesis, Durham University.
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We prove the Hasse principle for a smooth projective variety $X\subset \mathbb{P}^{n-1}_\mathbb{Q}$ defined by a smooth system of two cubic polynomials in $n\geq 39$ variables. The main tool here is the development of a version of Kloosterman refinement for a smooth system of equations defined over $\mathbb{Q}$.

Item Type Thesis (Doctoral)
Uncontrolled Keywords Number Theory, Algebraic Geometry, Circle Method, Hasse Principle
Divisions Faculty of Science > Mathematical Sciences, Department of
Date Deposited 08 Apr 2022 09:14
Last Modified 16 Mar 2026 18:33

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