Effective convergence bounds for Frobenius structures on connections

DOI10.4171/RSMUP/128-2zbMath1276.14032arXiv1111.0136OpenAlexW2963322049MaRDI QIDQ1947819

Kiran S. Kedlaya, Jan Tuitman

Publication date: 26 April 2013

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.0136

zbMATH Keywords

Picard-Fuchs equationGauss-Manin connectionFrobenius structureFrobenius lifteffective convergence bounds

Mathematics Subject Classification ID

Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Varieties over finite and local fields (11G25) Rigid analytic geometry (14G22) (p)-adic cohomology, crystalline cohomology (14F30) (p)-adic differential equations (12H25) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items

Frobenius structures on hypergeometric equations ⋮ Differential-algebraic equations and dynamic systems on manifolds ⋮ Unnamed Item ⋮ A numerical approach toward the \(p\)-adic Beilinson conjecture for elliptic curves over \(\mathbb{Q}\) ⋮ Improvements to the deformation method for counting points on smooth projective hypersurfaces ⋮ Counting points on curves using a map to $\mathbf {P}^1$ ⋮ Convergence Polygons for Connections on Nonarchimedean Curves ⋮ Frobenius action on a hypergeometric curve and an algorithm for computing values of Dwork's \(p\)-adic hypergeometric functions

Cites Work

• Rigid cohomology and \(p\)-adic point counting
• A Recursive Method for Computing Zeta Functions of Varieties
• Effective p-Adic Bounds for Solutions of Homogeneous Linear Differential Equations
• Unnamed Item