Galois theory for iterative connections and nonreduced Galois groups

DOI10.1090/S0002-9947-2010-04966-9zbMath1250.13009arXiv0712.3748MaRDI QIDQ3053479

Andreas Maurischat

Publication date: 29 October 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.3748

zbMATH Keywords

Galois theorydifferential Galois theoryconnectioninseparable extension

Mathematics Subject Classification ID

Derivations and commutative rings (13N15) Abstract differential equations (12H20) Inseparable field extensions (12F15) Modules of differentials (13N05) Galois theory and commutative ring extensions (13B05) Module categories and commutative rings (13C60)

Related Items (16)

Existence of \(\partial\)-parameterized Picard-Vessiot extensions over fields with algebraically closed constants ⋮ Picard-Vessiot theory of differentially simple rings ⋮ Reduced group schemes as iterative differential Galois groups ⋮ Additive group actions on affine \(\mathbb{T}\)-varieties of complexity one in arbitrary characteristic ⋮ A chain rule formula for higher derivations and inverses of polynomial maps ⋮ Difference Galois theory of linear differential equations ⋮ LARGE FIELDS IN DIFFERENTIAL GALOIS THEORY ⋮ Differential embedding problems over complex function fields ⋮ Frobenius modules and Galois representations ⋮ A general theory of André's solution algebras ⋮ Simply connected projective manifolds in characteristic \(p>0\) have no nontrivial stratified bundles ⋮ Generalized differentials and prolongation spaces ⋮ Torsion group schemes as iterative differential Galois groups ⋮ A categorical approach to Picard-Vessiot theory ⋮ Non-free iterative differential modules ⋮ Galois correspondence theorem for Picard-Vessiot extensions

Cites Work

• On the calculation of some differential Galois groups
• A Hopf algebraic approach to the Picard-Vessiot theory
• Picard-Vessiot extensions of Artinian simple module algebras.
• Fundamental group schemes for stratified sheaves
• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Première partie). Rédigé avec la colloboration de J. Dieudonné
• Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin
• Infinitesimal Group Scheme Actions on Finite Field Extensions
• Notes on Crystalline Cohomology. (MN-21)
• Différentielles non commutatives et théorie de Galois différentielle ou aux différences
• Iterative differential equations and the Abhyankar conjecture
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