Local metric properties and regular stratifications of p-adic definable sets
نویسندگان
چکیده
منابع مشابه
O ct 2 00 9 LOCAL METRIC PROPERTIES AND REGULAR STRATIFICATIONS OF p - ADIC DEFINABLE SETS
— We study the geometry of germs of definable (semialgebraic or subanalytic) sets over a p-adic field from the metric, differential and measure geometric point of view. We prove that the local density of such sets at each of their points does exist. We then introduce the notion of distinguished tangent cone with respect to some open subgroup with finite index in the multiplicative group of our ...
متن کاملLOCAL METRIC PROPERTIES AND REGULAR STRATIFICATIONS OF p-ADIC DEFINABLE SETS
— We study the geometry of germs of definable (semialgebraic or subanalytic) sets over a p-adic field from the metric, differential and measure geometric point of view. We prove that the local density of such sets at each of their points does exist. We then introduce the notion of distinguished tangent cone with respect to some open subgroup with finite index in the multiplicative group of our ...
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0.1. Let X be a scheme, reduced and separated, of finite type over Z. For p a prime number, one may consider the set X(Zp) of its Zp-rational points. For every n in N, there is a natural map πn : X(Zp)→ X(Z/p) assigning to a Zp-rational point its class modulo p. The image Yn,p of X(Zp) by πn is exactly the set of Z/p-rational points which can be lifted to Zp-rational points. Denote by Nn,p the ...
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Write OK for the valuation ting, MK for the maximal ideal of K and kK for the residue field. Let us fix $ some uniformizer of K. We denote by acm : K → OK/(MK) the map sending some nonzero x ∈ K to x$−ord(x) mod MK , and sending zero to zero. This is a definable map. We denote by RV the union of K×/(1 +MK) and {0} and by rv : K → RV the quotient map. More generally, if m ∈ N∗, we set RVm = K×/(...
متن کامل2 2 O ct 1 99 9 DEFINABLE SETS , MOTIVES AND P - ADIC INTEGRALS
Introduction 0.1. Let X be a scheme, reduced and separated, of finite type over Z. For p a prime number, one may consider the set X(Z p) of its Z p-rational points. For every n in N, there is a natural map π n : X(Z p) → X(Z/p n+1) assigning to a Z p-rational point its class modulo p n+1. The image Y n,p of X(Z p) by π n is exactly the set of Z/p n+1-rational points which can be lifted to Z p-r...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2012
ISSN: 0010-2571
DOI: 10.4171/cmh/275