scholarly journals Corrigendum: A curve selection lemma in spaces of arcs and the image of the Nash map

2021 ◽  
Vol 157 (3) ◽  
pp. 641-648
Author(s):  
Ana J. Reguera
Keyword(s):  
Perfect Field ◽  
Definition Of ◽  
Selection Lemma ◽  
Compositio Math ◽  
Curve Selection

The purpose of this note is to correct a mistake in the article “A curve selection lemma in spaces of arcs and the image of the Nash map” Compositio Math. 142 (2006), 119–130. It is due to an overlooked hypothesis in the definition of generically stable subset of the space of arcs X∞ of a variety X defined over a perfect field k.

The curve selection lemma and the Morse–Sard theorem

2009 ◽  
Vol 129 (3) ◽  
pp. 401-408 ◽  
Author(s):  
Carlos Gustavo Moreira ◽  
Maria Aparecida Soares Ruas
Keyword(s):  
Selection Lemma ◽  
Curve Selection

On the structure of semialgebraic sets over p-adic fields

1988 ◽  
Vol 53 (4) ◽  
pp. 1138-1164 ◽  
Author(s):  
Philip Scowcroft ◽  
Lou van den Dries
Keyword(s):  
Boolean Operations ◽  
Semialgebraic Sets ◽  
Algebraic Set ◽  
Real Algebraic Set ◽  
Open Set ◽  
Real Analytic ◽  
Selection Lemma ◽  
Image Position ◽  
Analytic Maps ◽  
Curve Selection

In his Singular points of complex hypersurfaces Milnor proves the following “curve selection lemma” [10, p. 25]:Let V ⊂ Rm be a real algebraic set, and let U ⊂ Rm be an open set defined by finitely many polynomial inequalities:Lemma 3.1. If U ∩ V contains points arbitrarily close to the origin (that is if 0 ∈ Closure (U ∩ V)) then there exists a real analytic curvewith p(0) = 0 and with p(t) ∈ U ∩ V for t > 0.Of course, this result will also apply to semialgebraic sets (finite unions of sets U ∩ V), and by Tarski's theorem such sets are exactly the sets obtained from real varieties by means of the finite Boolean operations and the projection maps Rn+1 → Rn. If, in this tiny extension of Milnor's result, we replace ‘R’ everywhere by ‘Qp’, we obtain a p-adic curve selection lemma, a version of which we will prove in this essay. Semialgebraic sets, in the p-adic context, may be defined just as they are over the reals: namely, as those sets obtained from p-adic varieties by means of the finite Boolean operations and the projection maps . Analytic maps are maps whose coordinate functions are given locally by convergent power series.

scholarly journals Quantitative curve selection lemma

2021 ◽  
Author(s):  
Saugata Basu ◽  
Marie-Françoise Roy
Keyword(s):  
Selection Lemma ◽  
Curve Selection

scholarly journals A curve selection lemma in spaces of arcs and the image of the Nash map

2006 ◽  
Vol 142 (01) ◽  
pp. 119-130 ◽  
Author(s):  
Ana J. Reguera
Keyword(s):  
Selection Lemma ◽  
Curve Selection

scholarly journals Chow motives without projectivity

2009 ◽  
Vol 145 (5) ◽  
pp. 1196-1226 ◽  
Author(s):  
Jörg Wildeshaus
Keyword(s):  
Shimura Varieties ◽  
Spectral Sequences ◽  
Perfect Field ◽  
Basic Properties ◽  
Structure Building ◽  
Princeton University ◽  
Chow Motives ◽  
Weight Structure ◽  
Compositio Math ◽  
Weight Structures

AbstractIn a recent paper, Bondarko [Weight structures vs. t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general), Preprint (2007), 0704.4003] defined the notion of weight structure, and proved that the category DMgm(k) of geometrical motives over a perfect field k, as defined and studied by Voevodsky, Suslin and Friedlander [Cycles, transfers, and motivic homology theories, Annals of Mathematics Studies, vol. 143 (Princeton University Press, Princeton, NJ, 2000)], is canonically equipped with such a structure. Building on this result, and under a condition on the weights avoided by the boundary motive [J. Wildeshaus, The boundary motive: definition and basic properties, Compositio Math. 142 (2006), 631–656], we describe a method to construct intrinsically in DMgm(k) a motivic version of interior cohomology of smooth, but possibly non-projective schemes. In a sequel to this work [J. Wildeshaus, On the interior motive of certain Shimura varieties: the case of Hilbert–Blumenthal varieties, Preprint (2009), 0906.4239], this method will be applied to Shimura varieties.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

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