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Durham e-Theses
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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)
Award:Doctor of Philosophy
Keywords:Number Theory, Algebraic Geometry, Circle Method, Hasse Principle
Faculty and Department:Faculty of Science > Mathematical Sciences, Department of
Thesis Date:2022
Copyright:Copyright of this thesis is held by the author
Deposited On:08 Apr 2022 10:14

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