ARITHMETIC ON A QUINTIC THREEFOLD

@article{Consani2001ARITHMETICOA,
  title={ARITHMETIC ON A QUINTIC THREEFOLD},
  author={Caterina Consani and Jasper L. J. Scholten},
  journal={International Journal of Mathematics},
  year={2001},
  volume={12},
  pages={943-972}
}
This paper investigates some aspects of the arithmetic of a quintic threefold in Pr4 with double points singularities. Particular emphasis is given to the study of the L-function of the Galois action ρ on the middle l-adic cohomology. The main result of the paper is the proof of the existence of a Hilbert modular form of weight (2, 4) and conductor 30, on the real quadratic field , whose associated (continuous system of) Galois representation(s) appears to be the most likely candidate to induce… 
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