Weak approximation on del Pezzo surfaces of degree 1

Details Weak approximation on del Pezzo surfaces of degree 1 Weak approximation on del Pezzo surfaces of degree 1

2008-01-16

arxiv.org/abs/0801.2430v2

Adv. Math. 219 (2008), 2123-2145

Mathematics

Number Theory

20 pages, no figures, Latex. Introduction revised to highlight Theorem 3.3; typos corrected. Magma scripts included at end of

Scientific paper

We study del Pezzo surfaces of degree 1 of the form w^2 = z^3 + Ax^6 + By^6
in the weighted projective space P_k(1,1,2,3), where k is a perfect field of
characteristic not 2 or 3 and A,B \in k^*. Over a number field, we exhibit an
infinite family of (minimal) counterexamples to weak approximation amongst
these surfaces, via a Brauer-Manin obstruction.

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