Places of algebraic function fields in arbitrary characteristic

DOI10.1016/j.aim.2003.07.021zbMath1134.12304arXiv1003.5686OpenAlexW1982786065MaRDI QIDQ1886580

Franz-Viktor Kuhlmann

Publication date: 18 November 2004

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

Full work available at URL: https://arxiv.org/abs/1003.5686

zbMATH Keywords

Large fieldsPlaces of algebraic function fieldsZariski space

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Valued fields (12J10)

Related Items

Kronecker Function Rings of Transcendental Field Extensions ⋮ The Zariski-Riemann Space of Valuation Rings ⋮ The algebra and model theory of tame valued fields ⋮ Small irreducible components of arc spaces in positive characteristic ⋮ NOTES ON EXTREMAL AND TAME VALUED FIELDS ⋮ Ultrafilter and Constructible Topologies on Spaces of Valuation Domains ⋮ Alexandroff topology of algebras over an integral domain ⋮ Elementary geometric local-global principles for fields ⋮ Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey ⋮ Density of composite places in function fields and applications to real holomorphy rings ⋮ The tree of quadratic transforms of a regular local ring of dimension two ⋮ Embeddings of function fields into ample fields ⋮ Axiomatizing the existential theory of \(\mathbb{F}_q((t))\) ⋮ Formal prime ideals of infinite value and their algebraic resolution ⋮ Witt equivalence of function fields over global fields ⋮ Characterization of extremal valued fields ⋮ Witt equivalence of fields: A survey with a special emphasis on applications of hyperfields ⋮ Affine schemes and topological closures in the Zariski-Riemann space of valuation rings ⋮ Suprema in spectral spaces and the constructible closure ⋮ Semistable reduction for overconvergentF-isocrystals, III: Local semistable reduction at monomial valuations ⋮ Every place admits local uniformization in a finite extension of the function field ⋮ Resolution of singularities of threefolds in positive characteristic. II ⋮ Abhyankar places admit local uniformization in any characteristic ⋮ The constructible topology on spaces of valuation domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Complete theories
• The Nullstellensatz over \(\mathfrak p\)-adically closed fields
• Embedding problems over large fields
• Valuation theory
• Maximal fields with valuations. I, II
• On the Valuations Centered in a Local Domain
• On places of algebraic function fields.
• Abhyankar places admit local uniformization in any characteristic
• La topologie du spectre réel
• Value groups, residue fields, and bad places of rational function fields
• Valuation theoretic and model theoretic aspects of local uniformization
• Prime Ideal Structure in Commutative Rings
• Some Applications of the Local Uniformization Theorem
• The compactness of the Riemann manifold of an abstract field of algebraic functions