Develops Kloosterman refinement for F_q(t) and uses it to establish quantitative arithmetic for rational points on smooth complete intersections of two quadrics in P^{n-1} for n>=9 and q odd.
Forms in many variables and differing degrees
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abstract
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral projective variety, provided only that its dimension is large enough in terms of its degree.
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math.NT 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Rational points on complete intersections over $\mathbb{F}_q(t)$
Develops Kloosterman refinement for F_q(t) and uses it to establish quantitative arithmetic for rational points on smooth complete intersections of two quadrics in P^{n-1} for n>=9 and q odd.