Valuation Theory in Interaction

Antonio Campillo; Franz-Viktor Kuhlmann; Bernard Teissier

doi:10.4171/149

BooksecrCollected Volume

Valuation Theory in Interaction

Editors

Antonio Campillo
Universidad de Valladolid, Spain
Franz-Viktor Kuhlmann
University of Saskatchewan, Saskatoon, Canada
Bernard Teissier
Institut de Mathématiques de Jussieu, Paris, France

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pp. 1–10
A study of irreducible polynomials over henselian valued fields via distinguished pairs
Kamal AghighAnuj BishnoiSudesh K. KhandujaSanjeev Kumar
pp. 11–15
On fields of totally $S$ -adic numbers. With an appendix by Florian Pop
Lior Bary-SorokerArno Fehm
pp. 16–54
Infinite towers of Artin-Schreier defect extensions of rational function fields
Anna Blaszczok
pp. 55–81
A refinement of Izumi's Theorem
Sébastien BoucksomCharles FavreMattias Jonsson
pp. 82–135
Multivariable Hodge theoretical invariants of germs of plane curves. II
Pierrette Cassou-NoguèsAnatoly Libgober
pp. 136–147
Existence des diviseurs dicritiques, d’après S.S. Abhyankar
Vincent CossartMickaël MatusinskiGuillermo Moreno-Socías
pp. 148–166
Invariants of the graded algebras associated to divisorial valuations dominating a rational surface singularity
Vincent CossartOlivier PiltantAna J. Reguera
pp. 167–207
An introduction to $C$ -minimal structures and their cell decomposition theorem
Pablo Cubides Kovacsics
pp. 208–218
Valuation semigroups of Noetherian local domains
Steven Dale Cutkosky
pp. 219–225
Additive polynomials over perfect fields
Salih Durhan
pp. 226–251
On $R$ -places and related topics
Danielle Gondard-Cozette
pp. 252–265
Extending valuations to formal completions
Francisco Javier Herrera GovantesMiguel Ángel Olalla AcostaMark SpivakovskyBernard Teissier
pp. 266–287
Extending real valuations to skew polynomial rings
Ángel GranjaM. C. MartínezC. Rodríguez
pp. 288–296
Stratifications in valued fields
Immanuel Halupczok
pp. 297–319
Imaginaries and definable types in algebraically closed valued fields
Ehud Hrushovski
pp. 320–349
Defects of algebraic function fields, completion defects and defect quotients
Franz-Viktor KuhlmannAsim Naseem
pp. 350–372
On generalized series fields and exponential-logarithmic series fields with derivations
Mickaël Matusinski
pp. 373–388
Jet schemes of rational double point singularities
Hussein Mourtada
pp. 389–403
Valuations centered at a two-dimensional regular local domain: infima and topologies
Josnei Novacoski
pp. 404–431
Reduction of local uniformization to the rank one case
Josnei NovacoskiMark Spivakovsky
pp. 432–463
Little survey on large fields - old & new
Florian Pop
pp. 464–473
Quasi-valuations -- topology and the weak approximation theorem
Shai Sarussi
pp. 474–565
Overweight deformations of affine toric varieties and local uniformization
Bernard Teissier
pp. 568–578
Detecting valuations using small Galois groups
Adam Topaz
pp. 579–595
Truncation in Hahn fields
Lou van den Dries
pp. 596–599
The ergodicity of 1-Lipschitz transformations on 2-adic spheres
Ekaterina Yurova
pp. 600–656
Ramification of higher local fields approaches and questions
Liang XiaoIgor Zhukov

Publication Date

1 September 2014

Identifiers

DOI: 10.4171/149
ISBN print: 978-3-03719-149-1
ISBN digital: 978-3-03719-649-6

Keywords

Valuation
defect
Abhyankar valuation
divisorial valuation
completion
local uniformization
toric geometry
key polynomial
excellent ring
local ring
valuation centered at a local domain
valuative tree
dicritical divisor
Rees valuation
Izumi’s theorem
plane curve singularity
Newton tree
rational surface singularity
Whitney stratification
jet scheme
embedded Nash problem
higher local field
wild ramification
dynamical system
irreducible polynomial
additive polynomial
Hilbertian field
large field
Galois theory
C-minimality
cell decomposition
imaginary element
formally real field
R-place
Hardy field
exponential-logarithmic series field
asymptotic integration
Hahn field
truncation
quasi-valuation.

Mathematics Subject Classification

12E30
12F10
13A18
14H20
14M25
11U09
12E05
12F05
12L12
13D40
13F30
13H05
13N15
14C20
14F10
14J17
16W60
32P05
37A05
54F50

Print

Hardcover, 670 pages, 17cm x 24cm