Arithmetic partial differential equations. I

DOI10.1016/j.aim.2009.12.026zbMath1217.12005OpenAlexW2049306853MaRDI QIDQ990746

Alexandru Buium, Santiago R. Simanca

Publication date: 1 September 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2009.12.026

zbMATH Keywords

elliptic curvesgroup schemespartial differential equationsFermat quotients

Mathematics Subject Classification ID

Local ground fields in algebraic geometry (14G20) Differential algebra (12H05) Abstract differential equations (12H20) Group schemes (14L15)

Related Items

Curvature on the integers. I. ⋮ Arithmetic partial differential equations. II ⋮ Arithmetic differential operators on \(\mathbb Z_p\) ⋮ The ring of differential Fourier expansions ⋮ Arithmetic Laplacians ⋮ Arithmetic differential equations in several variables

Cites Work

• Absolute derivations and zeta functions
• The analysis of linear partial differential operators. II: Differential operators with constant coefficients
• Differential characters of abelian varieties over \(p\)-adic fields
• Intersections in jet spaces and a conjecture of S. Lang
• Associative differential operations
• Differential characters and characteristic polynomial of Frobenius.
• Applications of analysis on nilpotent groups to partial differential equations
• Geometry of Differential Polynomial Functions, I: Algebraic Groups
• Geometry of Fermat adeles
• Differential modular forms
• Algebraic curves over fields with differentiation
• Differential Algebraic Groups
• Quantum calculus
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