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<p>We define projective hypersurfaces over finite fields associated to additive polynomials, and show that these are Frobenius superspecial. This means that some powers of the Frobenius endomorphism act on all their étale cohomology groups as scalar multiplication. As an immediate consequence, these hypersurfaces satisfy the semisimplicity conjecture.</p>

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Frobenius superspecial hypersurfaces associated to additive polynomials

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Takahiro Tsushima

摘要

We define projective hypersurfaces over finite fields associated to additive polynomials, and show that these are Frobenius superspecial. This means that some powers of the Frobenius endomorphism act on all their étale cohomology groups as scalar multiplication. As an immediate consequence, these hypersurfaces satisfy the semisimplicity conjecture.