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A non-selfdual 4-dimensional Galois representation

Jasper Scholten
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Abstract

In this paper it is explained how one can construct non-selfdual 4-dimensional $\ell$-adic Galois representations of Hodge type $h^{3,0}=h^{2,1}=h^{1,2}=h^{0,3}=1$, assuming a hypothesis concerning the cohomology of a certain threefold. For one such a representation the first 80000 coefficients of its $L$-function are computed, and it is numerically verified that this $L$-function satisfies a functional equation. Also a candidate for the conductor is obtained.

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Jasper Scholten. 1999-05-28. A non-selfdual 4-dimensional Galois representation. https://arxiv.org/abs/math/9905219

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