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.
Rational curves on cubic hypersurfaces over finite fields
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abstract
Given a smooth cubic hypersurface $X$ over a finite field of characteristic greater than 3 and two generic points on $X$, we use a function field analogue of the Hardy-Littlewood circle method to obtain an asymptotic formula for the number of degree $d$ rational curves on $X$ passing through those two points. We use this to deduce the dimension and irreducibility of the moduli space parametrising such curves, for large enough $d$.
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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.