Motivic cohomology of fat points in Milnor range via formal and rigid geometries

DOI10.1007/s00209-022-03122-4OpenAlexW3198296657WikidataQ114231047 ScholiaQ114231047MaRDI QIDQ2081433

Jin Hyun Park

Publication date: 13 October 2022

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

Full work available at URL: https://arxiv.org/abs/2108.13563

zbMATH Keywords

rigid geometryMilnor \(K\)-theorymotivic cohomologyChow groupalgebraic cyclealgebraic de Rham cohomologyformal schemeTate algebrasingular schemede Rham-Witt form

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Algebraic cycles (14C25) Higher symbols, Milnor (K)-theory (19D45) Formal power series rings (13F25) Formal neighborhoods in algebraic geometry (14B20)

Cites Work

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• A moving lemma for relative 0-cycles
• Algebraic cycles and higher K-theory
• Topological Stein factorization; cutting
• Milnor \(K\)-theory is the simplest part of algebraic \(K\)-theory
• Irreducible components of rigid spaces
• The additive dilogarithm
• Rigid analytic geometry and its applications
• Component groups of purely toric quotients.
• Milnor \(K\)-theory of rings, higher Chow groups and applications
• Motivic cohomology of fat points in Milnor range
• Foundations of rigid geometry. I
• \(K\)-theory and patching for categories of complexes
• Motives with modulus. III: The categories of motives
• Lectures on formal and rigid geometry
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
• Rigid analytic spaces
• Éléments de géométrie algébrique. I: Le langage des schémas. II: Étude globale élémentaire de quelques classe de morphismes. III: Étude cohomologique des faisceaux cohérents (première partie)
• The generalized de Rham-Witt complex over a field is a complex of zero-cycles
• Milnor 𝐾-theory of local rings with finite residue fields
• Regulators on additive higher Chow groups
• RECIPROCITY LAWS AND THE STABLE RANK OF POLYNOMIAL RINGS
• Higher Chow groups with modulus and relative Milnor $K$-theory
• HOMOLOGY OF THE FULL LINEAR GROUP OVER A LOCAL RING, AND MILNOR'SK-THEORY
• Motives with modulus, I: Modulus sheaves with transfers for non-proper modulus pairs
• Motives with modulus, II: Modulus sheaves with transfers for proper modulus pairs
• De Rham–Witt sheaves via algebraic cycles
• RELATIVE CYCLES WITH MODULI AND REGULATOR MAPS
• Motifs des variétés analytiques rigides
• Divisor class groups of singular surfaces
• Introduction to Algebraic K-Theory. (AM-72)
• On the De Rham cohomology of algebraic varieties
• On the De Rham cohomology of algebraic varieties