Séminaire Bourbaki, Vol. 48, 2005-2006, Exp. 952-966 by N. Bourbaki

By N. Bourbaki

Desk of Contents

Seminaire Bourbaki quantity forty eight web page 1 2005-2006 [doi UNKNOWN] Brion, Michel -- Compactification de l espace des modules des varietes abeliennes principalement polarisees

Seminaire Bourbaki quantity forty eight web page 33 2005-2006 [doi UNKNOWN] Burq, Nicolas -- Explosion pour l equation de Schroedinger au regime du log log

Seminaire Bourbaki quantity forty eight web page fifty five 2005-2006 [doi UNKNOWN] Huybrechts, Daniel -- Projectivity of Kaehler manifolds - Kodairas problem

Seminaire Bourbaki quantity forty eight web page seventy five 2005-2006 [doi UNKNOWN] Soule, Christophe -- Genres de Todd et valeurs aux entiers des derivees de fonctions L

Seminaire Bourbaki quantity forty eight web page ninety nine 2005-2006 [doi UNKNOWN] Wintenberger, Jean-Pierre -- los angeles conjecture de modularite de Serre : le cas de conducteur 1

Seminaire Bourbaki quantity forty eight web page 123 2005-2006 [doi UNKNOWN] Cornuejols, Gerard -- Le theoreme castle des graphes parfaits

Seminaire Bourbaki quantity forty eight web page 137 2005-2006 [doi UNKNOWN] Ducros, Antoine -- Espaces analytiques p-adiques au sens de Berkovich

Seminaire Bourbaki quantity forty eight web page 177 2005-2006 [doi UNKNOWN] Kowalski, Emmanuel -- Ecarts entre nombres premiers successifs

Seminaire Bourbaki quantity forty eight web page 211 2005-2006 [doi UNKNOWN] Lerner, Nicolas -- The verification of the Nirenberg-Treves conjecture

Seminaire Bourbaki quantity forty eight web page 237 2005-2006 [doi UNKNOWN] Vaes, Stefaan -- tension effects for Bernoulli activities and their von Neumann algebras

Seminaire Bourbaki quantity forty eight web page 295 2005-2006 [doi UNKNOWN] Christ, Michael -- Modulation invariant and multilinear singular necessary operators

Seminaire Bourbaki quantity forty eight web page 321 2005-2006 [doi UNKNOWN] Gruson, Caroline -- Sur les representations de size finie de l. a. tremendous algebre de Lie glm,n

Seminaire Bourbaki quantity forty eight web page 341 2005-2006 [doi UNKNOWN] Messing, William -- Travaux de Zink

Seminaire Bourbaki quantity forty eight web page 365 2005-2006 [doi UNKNOWN] Rodnianski, Igor -- The wave map challenge. Small info severe regularity

Seminaire Bourbaki quantity forty eight web page 385 2005-2006 [doi UNKNOWN] Yoccoz, Jean-Christophe -- Ensembles de Julia de mesure optimistic et disques de Siegel des polynomes quadratiques

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Additional resources for Séminaire Bourbaki, Vol. 48, 2005-2006, Exp. 952-966

Example text

Ash, D. Mumford, M. Rapoport & Y. Tai – Smooth compactification of locally symmetric varieties, Math. Sci. , 1975, Lie Groups: History, Frontiers and Applications, vol. IV. [7] S. Bosch, W. L¨ utkebohmert & M. Raynaud – N´eron models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 21, Springer-Verlag, Berlin, 1990. [8] G. -L. Chai – Degeneration of abelian varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 22, Springer-Verlag, Berlin, 1990, avec un appendice de D.

2 164 (1995), no. 22, p. 75–98 (English). [BW97] J. Bourgain & W. Wang – « Construction of blowup solutions for the nonlinear Schr¨ odinger equation with critical nonlinearity. », Ann. Scuola Norm. Sup. Pisa, Cl. , IV. Ser. 25 (1997), no. 1-2, p. 197–215 (English). [FMR04] G. Fibich, F. Merle & P. Raphael – « Numerical proof of a spectral property related to the singularity formation for the L2 critical non linear Schr¨ odinger equation », preprint, 2004. ´ E ´ MATHEMATIQUE ´ SOCIET DE FRANCE 2007 52 N.

L’id´ee g´en´erale est d’utiliser un profil auto-similaire pour d´ecrire la solution. Cependant, comme ces profils ne sont pas de norme L2 finie, il est n´ecessaire de les tronquer au bon endroit. Pour cela, on introduit des profils auto-similaires proches de l’´etat fondamental Q : on fixe un param`etre 0 < η < 1 (qui sera choisi petit par la suite) et pour b = 0 on d´efinit Rb = 2 |b| 1 + η, Rb− = 1−η 2 . |b| On fixe aussi une troncature radiale φb ´egale `a 0 pour |x| ≥ Rb et `a 1 pour |x| ≤ Rb− .

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