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Valuation Theory in Interaction

Campillo, Antonio,

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Valuation Theory in Interaction

Record Type:	Electronic resources : Monograph/item
Title/Author:	Valuation Theory in Interaction/ Antonio Campillo, Franz-Viktor Kuhlmann, Bernard Teissier
other author:	Campillo, Antonio,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2014,
Description:	1 online resource (670 pages)
Subject:	Fields & rings -
Online resource:	https://doi.org/10.4171/149
Online resource:	https://www.ems-ph.org/img/books/campillo_mini.gif
ISBN:	9783037196496

Valuation Theory in Interaction
Valuation Theory in Interaction[electronic resource] /Antonio Campillo, Franz-Viktor Kuhlmann, Bernard Teissier - Zuerich, Switzerland :European Mathematical Society Publishing House,2014 - 1 online resource (670 pages) - EMS Series of Congress Reports (ECR) ;2523-515X.

A study of irreducible polynomials over henselian valued fields via distinguished pairs /Kamal Aghigh, Anuj Bishnoi, Sudesh K. Khanduja, Sanjeev Kumar --

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

Having its classical roots, since more than a century, in algebraic number theory, algebraic geometry and the theory of ordered fields and groups, valuation theory has seen an amazing expansion into many other areas in recent decades. Moreover, having been dormant for a while in algebraic geometry, it has now been reintroduced as a tool to attack the open problem of resolution of singularities in positive characteristic and to analyse the structure of singularities. Driven by this topic, and by its many new applications in other areas, also the research in valuation theory itself has been intensified, with a particular emphasis on the deep open problems in positive characteristic. As important examples for the expansion of valuation theory, it has become extremely useful in the theory of complex dynamical systems, and in the study of non-oscillating trajectories of real analytic vector fields in three dimensions. Analogues of the Riemann-Zariski valuation spaces have been found to be the proper framework for questions of intersection theory in algebraic geometry and in the analysis of singularities of complex plurisubharmonic functions. In a different direction, the relation between Berkovich geometry, tropical geometry and valuation spaces, on the one hand, and the geometry of arc spaces and valuation spaces, on the other, have begun to deepen and clarify. Ever since its beginnings, valuation theory and Galois theory have grown closely together and influenced each other. Arguably, studying and understanding the extensions of valuations in algebraic field extensions is one of the most important questions in valuation theory, whereas using valuation theory is one of he most important tools in studying Galois extensions of fields, as well as constructing field extensions with given properties. The well established topic of the model theory of valued fields is also being transformed, in particular through the study of valued fields with functions and operators, a...

ISBN: 9783037196496

Standard No.: 10.4171/149doiSubjects--Topical Terms:

3480919
Fields & rings

Valuation Theory in Interaction
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245 1 0 $a Valuation Theory in Interaction $h [electronic resource] / $c Antonio Campillo, Franz-Viktor Kuhlmann, Bernard Teissier
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505 0 0 $t A study of irreducible polynomials over henselian valued fields via distinguished pairs / $r Kamal Aghigh, Anuj Bishnoi, Sudesh K. Khanduja, Sanjeev Kumar -- $t On fields of totally $\mathfrak{S}$-adic numbers. With an appendix by Florian Pop / $r Lior Bary-Soroker, Arno Fehm -- $t Infinite towers of Artin-Schreier defect extensions of rational function fields / $r Anna Blaszczok -- $t A refinement of Izumi's Theorem / $r Sébastien Boucksom, Charles Favre, Mattias Jonsson -- $t Multivariable Hodge theoretical invariants of germs of plane curves. II / $r Pierrette Cassou-Noguès, Anatoly Libgober -- $t Existence des diviseurs dicritiques, d'après S.S. Abhyankar / $r Vincent Cossart, Mickaël Matusinski, Guillermo Moreno-Socías -- $t Invariants of the graded algebras associated to divisorial valuations dominating a rational surface singularity / $r Vincent Cossart, Olivier Piltant, Ana J. Reguera -- $t An introduction to $C$-minimal structures and their cell decomposition theorem / $r Pablo Cubides Kovacsics -- $t Valuation semigroups of Noetherian local domains / $r Steven Dale Cutkosky -- $t Additive polynomials over perfect fields / $r Salih Durhan -- $t On $\mathbb{R}$-places and related topics / $r Danielle Gondard-Cozette -- $t Extending valuations to formal completions / $r Francisco Javier Herrera Govantes, Miguel Ángel Olalla Acosta, Mark Spivakovsky, Bernard Teissier -- $t Extending real valuations to skew polynomial rings / $r Ángel Granja, M. C. Martínez, C. Rodríguez -- $t Stratifications in valued fields / $r Immanuel Halupczok -- $t Imaginaries and definable types in algebraically closed valued fields / $r Ehud Hrushovski -- $t Defects of algebraic function fields, completion defects and defect quotients / $r Franz-Viktor Kuhlmann, Asim Naseem -- $t On generalized series fields and exponential-logarithmic series fields with derivations / $r Mickaël Matusinski -- $t Jet schemes of rational double point singularities / $r Hussein Mourtada -- $t Valuations centered at a two-dimensional regular local domain: infima and topologies / $r Josnei Novacoski -- $t Reduction of local uniformization to the rank one case / $r Josnei Novacoski, Mark Spivakovsky -- $t Little survey on large fields - old & new / $r Florian Pop -- $t Quasi-valuations -- topology and the weak approximation theorem / $r Shai Sarussi -- $t Overweight deformations of affine toric varieties and local uniformization / $r Bernard Teissier -- $t Detecting valuations using small Galois groups / $r Adam Topaz -- $t Truncation in Hahn fields / $r Lou van den Dries -- $t The ergodicity of 1-Lipschitz transformations on 2-adic spheres / $r Ekaterina Yurova -- $t Ramification of higher local fields approaches and questions / $r Liang Xiao, Igor Zhukov.
506 1 $a Restricted to subscribers: $u https://www.ems-ph.org/ebooks.php
520 $a Having its classical roots, since more than a century, in algebraic number theory, algebraic geometry and the theory of ordered fields and groups, valuation theory has seen an amazing expansion into many other areas in recent decades. Moreover, having been dormant for a while in algebraic geometry, it has now been reintroduced as a tool to attack the open problem of resolution of singularities in positive characteristic and to analyse the structure of singularities. Driven by this topic, and by its many new applications in other areas, also the research in valuation theory itself has been intensified, with a particular emphasis on the deep open problems in positive characteristic. As important examples for the expansion of valuation theory, it has become extremely useful in the theory of complex dynamical systems, and in the study of non-oscillating trajectories of real analytic vector fields in three dimensions. Analogues of the Riemann-Zariski valuation spaces have been found to be the proper framework for questions of intersection theory in algebraic geometry and in the analysis of singularities of complex plurisubharmonic functions. In a different direction, the relation between Berkovich geometry, tropical geometry and valuation spaces, on the one hand, and the geometry of arc spaces and valuation spaces, on the other, have begun to deepen and clarify. Ever since its beginnings, valuation theory and Galois theory have grown closely together and influenced each other. Arguably, studying and understanding the extensions of valuations in algebraic field extensions is one of the most important questions in valuation theory, whereas using valuation theory is one of he most important tools in studying Galois extensions of fields, as well as constructing field extensions with given properties. The well established topic of the model theory of valued fields is also being transformed, in particular through the study of valued fields with functions and operators, a...
650 0 7 $a Fields & rings $2 bicssc $3 3480919
650 0 7 $a Field theory and polynomials $2 msc $3 3480819
650 0 7 $a Order, lattices, ordered algebraic structures $2 msc $3 3481085
650 0 7 $a Commutative rings and algebras $2 msc $3 3480799
650 0 7 $a Algebraic geometry $2 bicssc $3 3480846
700 1 $a Campillo, Antonio, $e editor. $3 3481082
700 1 $a Kuhlmann, Franz-Viktor, $e editor. $3 3481083
700 1 $a Teissier, Bernard, $e editor. $3 3481084
856 4 0 $u https://doi.org/10.4171/149
856 4 2 $3 cover image $u https://www.ems-ph.org/img/books/campillo_mini.gif