Topology and arithmetic of resultants, II: The resultant 1 hypersurface
نویسندگان
چکیده
منابع مشابه
Topology and arithmetic of resultants , II : the resultant = 1 hypersurface Benson Farb and Jesse Wolfson
We consider the moduli space Rn of pairs of monic, degree n polynomials whose resultant equals 1. We relate the topology of these algebraic varieties to their geometry and arithmetic. In particular, we compute their étale cohomology, the associated eigenvalues of Frobenius, and the cardinality of their set of Fq-points. When q and n are coprime, we show that the étale cohomology of Rn/Fq is pur...
متن کاملTopology and arithmetic of resultants , II : the resultant = 1 hypersurface Benson Farb and Jesse Wolfson ∗ With an appendix by Christophe Cazanave
We consider the moduli space Rn of pairs of monic, degree n polynomials whose resultant equals 1. We relate the topology of these algebraic varieties to their geometry and arithmetic. In particular, we compute their étale cohomology, the associated eigenvalues of Frobenius, and the cardinality of their set of Fq-points. When q and n are coprime, we show that the étale cohomology of Rn/Fq is pur...
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We consider the interplay of point counts, singular cohomology, étale cohomology, eigenvalues of the Frobenius and the Grothendieck ring of varieties for two families of varieties: spaces of rational maps and moduli spaces of marked, degree d rational curves in P. We deduce as special cases algebro-geometric and arithmetic refinements of topological computations of Segal, Cohen–Cohen–Mann–Milgr...
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ژورنال
عنوان ژورنال: Algebraic Geometry
سال: 2017
ISSN: 2214-2584
DOI: 10.14231/ag-2017-019