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Zeta functions of
nondegenerate hypersurfaces in toric varieties via controlled
reduction in $p$-adic cohomology
Edgar Costa, David Harvey and Kiran S. Kedlaya |
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Vol. 2 (2019), No. 1, 221–238
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Abstract |
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We give an interim report on some improvements and generalizations of the Abbott–Kedlaya–Roe method to compute the zeta function of a nondegenerate ample hypersurface in a projectively normal toric variety over in linear time in . These are illustrated with a number of examples including K3 surfaces, Calabi–Yau threefolds, and a cubic fourfold. The latter example is a nonspecial cubic fourfold appearing in the Ranestad–Voisin coplanar divisor on moduli space; this verifies that the coplanar divisor is not a Noether–Lefschetz divisor in the sense of Hassett. |
Keywords
zeta function, toric varieties, Kedlaya's algorithm,
$p$-adic methods
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Mathematical Subject Classification 2010
Primary: 11G25
Secondary: 11M38, 11Y16, 14G10
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Milestones
Received: 1 March 2018
Revised: 24 August 2018
Accepted: 4 September 2018
Published: 13 February 2019
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Authors |
| Edgar Costa | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| David Harvey | |
| School of Mathematics and
Statistics University of New South Wales Sydney Australia |
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| Kiran S. Kedlaya | |
| Department of Mathematics University of California, San Diego La Jolla, CA United States |
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