A heuristic for the distribution of point counts for random curves over a finite field

DOI10.1098/rsta.2014.0310zbMath1397.11108arXiv1410.7373OpenAlexW3106224243WikidataQ42559276 ScholiaQ42559276MaRDI QIDQ2955767

Jeffrey D. Achter, Daniel Erman, Kiran S. Kedlaya, Melanie Matchett Wood, David Zureick-Brown

Publication date: 13 January 2017

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.7373

zbMATH Keywords

Poisson distributioncohomology of moduli spacesrandom algebraic curve

Mathematics Subject Classification ID

Combinatorial probability (60C05) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15)

Related Items (4)

Motivic random variables and representation stability. II: Hypersurface sections ⋮ Number fields and function fields: coalescences, contrasts and emerging applications ⋮ How large is \(A_g(\mathbb F_q)\)? ⋮ Distributions of Traces of Frobenius for Smooth Plane Curves Over Finite Fields

Cites Work

• Unnamed Item
• Distribution of zeta zeroes of Artin-Schreier covers
• The Lefschetz trace formula for algebraic stacks
• Fluctuations in the number of points on smooth plane curves over finite fields
• The fluctuations in the number of points on a family of curves over a finite field
• Stability of the homology of the moduli spaces of Riemann surfaces with spin structure
• The fluctuations in the number of points on a hyperelliptic curve over a finite field
• Stability of the homology of the mapping class groups of orientable surfaces
• The Euler characteristic of the moduli space of curves
• On the distribution of zeroes of Artin-Schreier \(L\)-functions
• The probability that a complete intersection is smooth
• The stable moduli space of Riemann surfaces: Mumford's conjecture
• The irreducibility of the space of curves of a given genus
• Gaussian Point Count Statistics for Families of Curves Over a Fixed Finite Field
• Statistics for Traces of Cyclic Trigonal Curves over Finite Fields
• On the Eigenvalues of Random Matrices
• Twisted Bundles and Admissible Covers
• The Distribution of the Number of Points on Trigonal Curves over 𝔽q

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