Towards the Sato–Tate groups of trinomial hyperelliptic curves

DOI10.1142/S1793042121500822zbMath1474.11121arXiv1812.00242MaRDI QIDQ5157556

Melissa Emory, Alexandre Peyrot, Heidi Goodson

Publication date: 19 October 2021

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.00242

zbMATH Keywords

hyperelliptic curveabelian varietiesStickelberger's congruenceSato-Tate group

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items (2)

Non-isogenous abelian varieties sharing the same division fields ⋮ Sato-Tate distributions of \(y^2=x^p-1\) and \(y^2=x^{2p}-1\)

Uses Software

• Magma
• CoCalc

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A family of Calabi-Yau varieties and potential automorphy. II.
• A family of Calabi-Yau varieties and potential automorphy
• Algebraic cycles on Abelian varieties of Fermat type
• Idempotent relations and factors of Jacobians
• The Magma algebra system. I: The user language
• The twisting Sato-Tate group of the curve \(y^2 = x^{8} - 14x^4 + 1\)
• La conjecture de Weil. I
• Jacobi sums and Stickelberger's congruence
• Sato-Tate distributions of twists of the Fermat and the Klein quartics
• Decomposing Jacobians of curves over finite fields in the absence of algebraic structure
• Introduction to Abelian Varieties
• Sato–Tate distributions and Galois endomorphism modules in genus 2
• Sato-Tate groups of 𝑦²=𝑥⁸+𝑐 and 𝑦²=𝑥⁷-𝑐𝑥.
• Hypergeometric functions over ${\mathbb {F}_p}$ and relations to elliptic curves and modular forms
• Equations for the Jacobian of a hyperelliptic curve
• ℓ-adic algebraic monodromy groups, cocharacters, and the MumfordTate conjecture
• Pell and Pell–Lucas Numbers with Applications

This page was built for publication: Towards the Sato–Tate groups of trinomial hyperelliptic curves