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The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type .
We generalize L. J. Mordell’s construction of cubic surfaces for which the Hasse principle fails.
In this paper, we give a numerical characterization of nef arithmetic -Cartier divisors of -type on an arithmetic surface. Namely an arithmetic -Cartier divisor of -type is nef if and only if is pseudo-effective and .
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