Real and \(p\)-adic Picard-Vessiot fields

DOI10.1007/s00208-015-1272-2zbMath1344.34096arXiv1307.2388OpenAlexW1762408251MaRDI QIDQ289825

Marius van der Put, Zbigniew Hajto, Teresa Crespo

Publication date: 31 May 2016

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.2388

zbMATH Keywords

differential modulefield extensionfield of constantsPicard-Vessiot field

Mathematics Subject Classification ID

(p)-adic differential equations (12H25) Abstract differential equations (12H20) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Galois cohomology (11R34) Forms over real fields (11E10)

Related Items (11)

Real Liouvillian extensions of partial differential fields ⋮ Real difference Galois theory ⋮ On differential Galois groups of strongly normal extensions ⋮ On the differential transcendentality of the Morita \(p\)-adic gamma function ⋮ LARGE FIELDS IN DIFFERENTIAL GALOIS THEORY ⋮ Differential embedding problems over Laurent series fields ⋮ Embedded Picard–Vessiot extensions ⋮ Differential Galois groups over Laurent series fields ⋮ Picard-Vessiot extensions of real differential fields ⋮ Real Liouville Extensions ⋮ Differential Galois cohomology and parameterized Picard–Vessiot extensions

Cites Work

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• Formally \(p\)-adic fields
• An introduction to real algebra
• Hodge cycles, motives, and Shimura varieties
• Galois Cohomology
• Connected linear groups as differential Galois groups
• Contribution to the Picard-Vessiot Theory of Homogeneous Linear Differential Equations
• Linear algebraic groups.

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