Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology
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Publication:6165868
DOI10.2140/obs.2019.2.221zbMath1520.14095arXiv1806.00368OpenAlexW3100268685MaRDI QIDQ6165868
David Harvey, Kiran S. Kedlaya, Edgar Costa
Publication date: 2 August 2023
Published in: The Open Book Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1806.00368
Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Varieties over finite and local fields (11G25) (p)-adic cohomology, crystalline cohomology (14F30) Zeta and (L)-functions in characteristic (p) (11M38)
Related Items (6)
Root repulsion and faster solving for very sparse polynomials over \(p\)-adic fields ⋮ \(L\)-functions of elliptic curves modulo integers ⋮ On reconstructing subvarieties from their periods ⋮ A Numerical Transcendental Method in Algebraic Geometry: Computation of Picard Groups and Related Invariants ⋮ Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus ⋮ Deep learning Gauss-Manin connections
Cites Work
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- Genus 2 point counting over prime fields
- Variety of power sums and divisors in the moduli space of cubic fourfolds
- An extension of Kedlaya's algorithm for hyperelliptic curves
- Complete classification of reflexive polyhedra in four dimensions
- \(K3\) surfaces over finite fields with given \(L\)-function
- Hypersurface simple K3 singularities
- Counting points on \(C_{ab}\) curves using Monsky-Washnitzer cohomology
- Improvements to the deformation method for counting points on smooth projective hypersurfaces
- Point counting in families of hyperelliptic curves
- Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori
- Polyedres de Newton et nombres de Milnor
- Zeta-function of monodromy and Newton's diagram
- Classification of reflexive polyhedra in three dimensions
- On the Hodge structure of projective hypersurfaces in toric varieties
- Finiteness and cohomological purity in rigid cohomology (with an appendix by Aise Johan de Jong)
- The Magma algebra system. I: The user language
- Counting solutions to equations in many variables over finite fields
- Counting points on curves using a map to \(\mathbf P^1\). II.
- Counting points on hyperelliptic curves in average polynomial time
- An extension of Kedlaya's algorithm to hyperelliptic curves in characteristic \(2\)
- Formal cohomology. I
- Formal cohomology. II: The cohomology sequence of a pair
- On the zeta function of a hypersurface. I
- Formal cohomology. III: Fixed point theorems
- On the periods of certain rational integrals. I, II
- Counting points on curves using a map to $\mathbf {P}^1$
- Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time
- Counting Points on Genus 2 Curves with Real Multiplication
- Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time, II
- Computing zeta functions of nondegenerate curves
- Computing zeta functions of arithmetic schemes
- Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
- Logarithmic structures of Fontaine-Illusie. II
- Computing zeta functions of generic projective hypersurfaces in larger characteristic
- Deformation theory and the computation of zeta functions
- Computing zeta functions of nondegenerate hypersurfaces with few monomials
- Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
- Cubic Fourfolds, K3 Surfaces, and Rationality Questions
- Advances in Cryptology - EUROCRYPT 2004
- Kedlaya's Algorithm in Larger Characteristic
- Relative Rigid Cohomology and Deformation of Hypersurfaces
- Variation of Néron–Severi Ranks of Reductions of K3 Surfaces
- Compactifications of subvarieties of tori
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