On Kato and Kuzumaki's properties for the Milnor \(K_2\) of function fields of \(p\)-adic curves

DOI10.2140/ant.2024.18.815arXiv2206.04214OpenAlexW4392195059MaRDI QIDQ6122205

Diego Izquierdo, Giancarlo Lucchini Arteche

Publication date: 28 February 2024

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.04214

zbMATH Keywords

Galois cohomologycohomological dimensionFano hypersurfacesMilnor \(K\)-theoryzero-cycles\(C_i\) property\(p\)-adic function fields

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Cohomological dimension of fields (12G10) Galois cohomology (12G05) Rational points (14G05) Curves over finite and local fields (11G20) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Fano varieties (14J45) Hypersurfaces and algebraic geometry (14J70) Steinberg groups and (K_2) (19C99) Generalized class field theory ((K)-theoretic aspects) (19F05)

Cites Work

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• Duality theorems for function fields over higher local fields
• Hasse principle and weak approximation for multinorm equations
• On a conjecture of Kato and Kuzumaki concerning Fano hypersurfaces
• On motivic cohomology with \(\mathbb{Z}/l\)-coefficients
• Motivic cohomology over Dedekind rings
• Local class field theory via Lubin-Tate theory
• The dimension of fields and algebraic \(K\)-theory
• Algebraic cycles and higher K-theory
• Milnor \(K\)-theory is the simplest part of algebraic \(K\)-theory
• Patching and local-global principles for homogeneous spaces over function fields of \(p\)-adic curves
• Classes of motivic étale cycles
• The \(K\)-theory of fields in characteristic \(p\)
• Norm varieties
• On a conjecture of Kato and Kuzumaki
• On quasi algebraic closure
• Index of varieties over Henselian fields and Euler characteristic of coherent sheaves
• Note on a paper of Lang concerning quasi algebraic closure
• Lectures on Resolution of Singularities (AM-166)
• Field Arithmetic
• A Hasse principle for two dimensional global fields.
• Néron Models
• SURFACES DE DEL PEZZO SANS POINT RATIONNEL SUR UN CORPS DE DIMENSION COHOMOLOGIQUE UN
• The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky
• Central Simple Algebras and Galois Cohomology

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