| 1. |
- Hosgood, Tim, 1994-
(författare)
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La théorie de Chern–Weil simpliciale pour les faisceaux analytiques cohérents, partie 1
- 2023
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Ingår i: Bulletin de la Société Mathématique de France. - 0037-9484 .- 2102-622X. ; 151:1, s. 127-170
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Tidskriftsartikel (refereegranskat)abstract
- In Chern classes for coherent sheaves, H.I. Green constructs Chern classes in de Rham cohomology of coherent analytic sheaves. We construct here a formal (infinity, 1)-categorical framework into which we can place Green's work and generalise it, also obtaining a better idea as to what exactly a simplicial connection should be. The result will be the ability to work with generalised invariant polynomials (which will be introduced in the sequel to this paper) evaluated at the curvature of so-called admissible simplicial connections to get explicit Cech representatives in de Rham cohomology of characteristic classes of coherent analytic sheaves.
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| 2. |
- Janson, Svante, 1955-, et al.
(författare)
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A piecewise contractive dynamical system and Phragmèn's election method
- 2019
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Ingår i: Bulletin de la Société Mathématique de France. - : FRENCH MATHEMATICAL SOC. - 0037-9484 .- 2102-622X. ; 147:3, s. 395-441
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Tidskriftsartikel (refereegranskat)abstract
- We prove some basic results for a dynamical system given by a piece-wise linear and contractive map on the unit interval that takes two possible values at a point of discontinuity. We prove that there exists a universal limit cycle in the non-exceptional cases, and that the exceptional parameter set is very tiny in terms of gauge functions. The exceptional two-dimensional parameter is shown to have Hausdorff-dimension one. We also study the invariant sets and the limit sets; these are sometimes different and there are several cases to consider. In addition, we prove the existence of a unique invariant measure. We apply some of our results for the dynamical system, involving a study of rational and irrational rotation numbers, to a combinatorial problem involving an election method suggested by Phragmen, and we show that the proportion of elected seats for each party converges to a limit, which is a rational number except for a very small exceptional set of parameters.
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| 3. |
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| 4. |
- Rydh, David, 1980-
(författare)
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Submersions and effective descent of étale morphisms
- 2010
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Ingår i: Bulletin de la Société Mathématique de France. - Paris : Société mathématique de France. - 0037-9484 .- 2102-622X. ; 138:2, s. 181-230
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Tidskriftsartikel (refereegranskat)abstract
- Using the flatification by blow-up result of Raynaud and Gruson, we obtain new results for submersive and subtrusive morphisms. We show that universally subtrusive morphisms, and in particular universally open morphisms, are morphisms of effective descent for the fibered category of étale morphisms. Our results extend and supplement previous treatments on submersive morphisms by Grothendieck, Picavet and Voevodsky. Applications include the universality of geometric quotients and the elimination of noetherian hypotheses in many instances.
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| 5. |
- Wagner, Stefan, PhD, 1982-
(författare)
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SECONDARY CHARACTERISTIC CLASSES OF LIE ALGEBRA EXTENSIONS
- 2019
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Ingår i: Bulletin de la Société Mathématique de France. - : FRENCH MATHEMATICAL SOC. - 0037-9484 .- 2102-622X. ; 147:3, s. 443-453
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the notion of secondary characteristic classes of Lie algebra extensions. As an application of our construction we obtain a new proof of Lecomte's generalization of the Chern-Weil homomorphism.
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