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تسجيل مستخدم جديدA motivic local Cauchy-Crofton formula
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تأليف
Arthur Forey
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In this note, we establish a version of the local Cauchy-Crofton formula for definable sets in Henselian discretely valued fields of characteristic zero. It allows to compute the motivic local density of a set from the densities of its projections integrated over the Grassmannian.
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e assumes H to be a generic hyperplane section. Hence the proofs of all results starting from 2.3 contain gaps. The author hopes to correct this (somehow) in a future version. At least, most of the results follow from certain standard motivic conjectures (see part 1 of Remark 3.2.4 in the previous version). If the author would not find a way to prove Theorems 2.3.1 and 2.3.2 (without 2.1.1), then in the next version of the preprint the results of section 4 will be deduced from certain conjectures; certainly this is not a very exiting result.
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