AsterisquePub Date : 2018-11-22DOI: 10.24033/ast.11101
Joel W. Fish, H. Hofer
{"title":"Exhaustive Gromov compactness for pseudoholomorphic curves","authors":"Joel W. Fish, H. Hofer","doi":"10.24033/ast.11101","DOIUrl":"https://doi.org/10.24033/ast.11101","url":null,"abstract":"Here we extend the notion of target-local Gromov convergence of pseudoholomorphic curves to the case in which the target manifold is not compact, but rather is exhausted by compact neighborhoods. Under the assumption that the curves in question have uniformly bounded area and genus on each of the compact regions (but not necessarily global bounds), we prove a subsequence converges in an exhaustive Gromov sense.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45419561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2018-11-06DOI: 10.24033/AST.963
P. Deligne
{"title":"Comptage de faisceaux $l$-adiques","authors":"P. Deligne","doi":"10.24033/AST.963","DOIUrl":"https://doi.org/10.24033/AST.963","url":null,"abstract":"1.2. Dans l’article [Dr], qui reste pour moi aussi mystérieux qu’il y a 31 ans, Drinfeld calcule le nombre de points fixes de φ : E → E. Un Q̄l-faisceau L0 de rang un sur Spec(Fq) est déterminé à isomorphisme près par l’unité λ de Q̄l telle que le Frobenius géométrique Fr ∈ Gal(F/Fq) agisse par multiplication par λ sur la fibre de L0 au point géométrique Spec(F). La Fq-torsion de F0 sur X0 par L0 est le produit tensoriel avec l’image inverse de L0 sur X0. Par abus de langage, on dira aussi “Fq-torsion par λ”. Drinfeld utilise que la classe d’isomorphie d’un Q̄l-faisceau lisse F sur X est fixe par Frob si et seulement si F est l’image inverse d’un Q̄l-faisceau F0 sur X0, et que, si F","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68830862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2018-10-31DOI: 10.24033/ast.11106
D. Sullivan
{"title":"Lattice Hydrodynamics","authors":"D. Sullivan","doi":"10.24033/ast.11106","DOIUrl":"https://doi.org/10.24033/ast.11106","url":null,"abstract":"Using the combinatorics of two interpenetrating face centered cubic lattices together with the part of calculus naturally encoded in combinatorial topology, we construct from first principles a lattice model of 3D incompressible hydrodynamics on triply periodic three space. Actually the construction applies to every dimension, but has special duality features in dimension three.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45038681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2018-09-25DOI: 10.24033/ast.1088
Antoine Chambert-Loir
{"title":"Relations de Hodge-Riemann et combinatoire des matroïdes","authors":"Antoine Chambert-Loir","doi":"10.24033/ast.1088","DOIUrl":"https://doi.org/10.24033/ast.1088","url":null,"abstract":"Finite matroids are combinatorial structures that express the concept of linear independence. In 1964, G.-C. Rota conjectured that the coefficients of the\"characteristic polynomial\"of a matroid $M$, polynomial whose coefficients enumerate its subsets of given rank, form a log-concave sequence. K. Adiprasito, J. Huh et E. Katz have proved this conjecture using methods which, although entirely combinatorial, are inspired by algebraic geometry. From the Bergman fan of the matroid $M$, they define a graded\"Chow ring\"$A(M)$ for which they prove analogs of the Poincar'e duality, the Hard Lefschetz theorem, and the Hodge--Riemann relations. The sought for log-concavity inequalities are then analogous to the Khovanskii--Teissier inequalities.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44670660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2018-07-31DOI: 10.24033/ast.1090
Jean-Pierre Serre
{"title":"Distribution asymptotique des valeurs propres des endomorphismes de Frobenius d'après Abel, Chebyshev, Robinson,...","authors":"Jean-Pierre Serre","doi":"10.24033/ast.1090","DOIUrl":"https://doi.org/10.24033/ast.1090","url":null,"abstract":"We consider unitary polynomials $P in Z[X]$ whose roots $(x_i)$ belong to a given compact $K$ of $C$. To such a polynomial we associate the measure $mu_P$ on $K$ which is the mean value of the Dirac measures $delta_{x_i}$. What are the limits of the measures $mu_P$ when $P$ varies ? In particular, what are their supports? We give partial answers to such questions, especially when $K$ is contained in $R$.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41335811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2018-05-15DOI: 10.24033/ast.1146
B. Bhatt, J. Lurie, A. Mathew
{"title":"Revisiting the de Rham-Witt complex","authors":"B. Bhatt, J. Lurie, A. Mathew","doi":"10.24033/ast.1146","DOIUrl":"https://doi.org/10.24033/ast.1146","url":null,"abstract":"The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p$. \u0000We introduce a category of cochain complexes equipped with an endomorphism $F$ (of underlying graded abelian groups) satisfying $dF = pFd$, whose homological algebra we study in detail. To any such object satisfying an abstract analog of the Cartier isomorphism, an elementary homological process associates a generalization of the de Rham-Witt construction. Abstractly, the homological algebra can be viewed as a calculation of the fixed points of the Berthelot-Ogus operator $L eta_p$ on the $p$-complete derived category. We give various applications of this approach, including a simplification of the crystalline comparison in $A Omega$-cohomology theory.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42912789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2018-02-16DOI: 10.24033/AST.11113
Ricardo P'erez-Marco
{"title":"On quasi-invariant curves","authors":"Ricardo P'erez-Marco","doi":"10.24033/AST.11113","DOIUrl":"https://doi.org/10.24033/AST.11113","url":null,"abstract":"Quasi-invariant curves are used in the study of hedgehog dynamics. Denjoy-Yoccoz lemma is the preliminary step for Yoccoz's complex renormalization techniques for the study of linearization of analytic circle diffeomorphisms. We give a geometric interpretation of Denjoy-Yoccoz lemma using the hyperbolic metric that gives a direct construction of quasi-invariant curves without renormalization.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43602960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2018-01-01DOI: 10.24033/AST.1056
Laurent Fargues, J. Fontaine, préface de Pierre Colmez
{"title":"Courbes et fibrés vectoriels en théorie de Hodge p-adique","authors":"Laurent Fargues, J. Fontaine, préface de Pierre Colmez","doi":"10.24033/AST.1056","DOIUrl":"https://doi.org/10.24033/AST.1056","url":null,"abstract":"Dans ce travail nous definissons et etudions la courbe fondamentale en theorie de Hodge p-adique. Nous demontrons un theoreme de classification des fibres vectoriels sur celle-ci et nous en deduisons de nouvelles preuves des deux theoremes fondamentaux de la theorie de Hodge p-adique: faiblement admissible implique admissible et e theoreme de la monodromie p-adique.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68827666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2017-12-08DOI: 10.24033/AST.11118
B. Fayad, Jean-Pierre Marco, D. Sauzin, Jean-Pierre Marco
{"title":"Attracted by an elliptic fixed point","authors":"B. Fayad, Jean-Pierre Marco, D. Sauzin, Jean-Pierre Marco","doi":"10.24033/AST.11118","DOIUrl":"https://doi.org/10.24033/AST.11118","url":null,"abstract":"We give examples of symplectic diffeomorphisms of R^6 for which the origin is a non-resonant elliptic fixed point which attracts an orbit.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48417152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AsterisquePub Date : 2017-11-08DOI: 10.24033/ast.1147
Tom Bachmann, Marc Hoyois
{"title":"Norms in motivic homotopy theory","authors":"Tom Bachmann, Marc Hoyois","doi":"10.24033/ast.1147","DOIUrl":"https://doi.org/10.24033/ast.1147","url":null,"abstract":"If $f : S' to S$ is a finite locally free morphism of schemes, we construct a symmetric monoidal \"norm\" functor $f_otimes : mathcal{H}_{bullet}(S')to mathcal{H}_{bullet}(S)$, where $mathcal{H}_bullet(S)$ is the pointed unstable motivic homotopy category over $S$. If $f$ is finite étale, we show that it stabilizes to a functor $f_otimes : mathcal{S}mathcal{H}(S') to mathcal{S}mathcal{H}(S)$, where $mathcal{S}mathcal{H}(S)$ is the $mathbb{P}^1$-stable motivic homotopy category over $S$. Using these norm functors, we define the notion of a normed motivic spectrum, which is an enhancement of a motivic $E_infty$-ring spectrum. The main content of this text is a detailed study of the norm functors and of normed motivic spectra, and the construction of examples. In particular: we investigate the interaction of norms with Grothendieck's Galois theory, with Betti realization, and with Voevodsky's slice filtration; we prove that the norm functors categorify Rost's multiplicative transfers on Grothendieck-Witt rings; and we construct normed spectrum structures on the motivic cohomology spectrum $Hmathbb{Z}$, the homotopy $K$-theory spectrum $KGL$, and the algebraic cobordism spectrum $MGL$. The normed spectrum structure on $Hmathbb{Z}$ is a common refinement of Fulton and MacPherson's mutliplicative transfers on Chow groups and of Voevodsky's power operations in motivic cohomology.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42046211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}