Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.725009
Title: Non-archimedean stratifications in T-convex fields
Author: Garcia Ramirez, Erick
ISNI:       0000 0004 6422 0483
Awarding Body: University of Leeds
Current Institution: University of Leeds
Date of Award: 2017
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Abstract:
We prove that whenever T is a power-bounded o-minimal theory, t-stratifications exist for definable maps and sets in T-convex fields. To this effect, a thorough analysis of definability in T-convex fields is carried out. One of the conditions required for the result above is the Jacobian property, whose proof in this work is a long and technical argument based on an earlier proof of this property for valued fields with analytic structure. An example is given to illustrate that t-stratifications do not exist in general when T is not power-bounded. We also show that if T is power-bounded, the theory of all T-convex fields is b-minimal with centres. We also address several applications of tstratifications. For this we exclusively work with a power-bounded T. The first application establishes that a t-stratification of a definable set X in a T-convex field induces t stratifications on the tangent cones of X. This is a contribution to local geometry and singularity theory. Regarding R as a model of T, the remaining applications are derived by considering the stratifications induced on R by t-stratifications in non-standard models. We prove that each such induced stratification is a C1-Whitney stratification; this in turn leads to a new proof of the existence of Whitney stratifications for definable sets in R. We also deal with interactions between tangent cones of definable sets in R and stratifications.
Supervisor: Halupczok, Immanuel ; Macpherson, H. Dugald Sponsor: CONACYT ; DGRI-SEP
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.725009  DOI: Not available
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