{"title":"Corrigendum: On the first restricted cohomology of a reductive Lie algebra and its Borel subalgebras","authors":"R. Tange","doi":"10.5802/aif.3310","DOIUrl":"https://doi.org/10.5802/aif.3310","url":null,"abstract":"Lemma. Let S be a Noetherian commutative ring, let R be a Noetherian subring of S which is a domain such that R∩ n ∈ Maxspec(R) for all n ∈ Maxspec(S), and let N be a finitely generated S-module which is flat over R. (i) Let M be an S-submodule of N with (mN) ∩ M ⊆ mM for all m ∈ Maxspec(R). Then N/M is a torsion-free R-module. (ii) Let M be an S-module, let φ : M → N be an S-linear map. Assume that for all m ∈ Maxspec(R) the canonical map M → M/mM maps Ker(φ) onto the kernel of the induced R/m-linear map φ : M/mM → N/mN . Then N/Im(φ) is a torsion-free R-module.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":"70 1","pages":"169-170"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71208871","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}
{"title":"Large degree covers and sharp resonances of hyperbolic surfaces","authors":"D. Jakobson, Fr'ed'eric Naud, Louis Soares","doi":"10.5802/aif.3319","DOIUrl":"https://doi.org/10.5802/aif.3319","url":null,"abstract":"— Let Γ be a convex co-compact discrete group of isometries of the hyperbolic plane H2, and X = ΓH2 the associated surface. In this paper we investigate the behaviour of resonances of the Laplacian ∆X̃ for large degree covers of X given by X̃ = Γ̃H2 where Γ̃ C Γ is a finite index normal subgroup of Γ. Using techniques of thermodynamical formalism and representation theory, we prove two new existence results of sharp non-trivial resonances close to {Re(s) = δ}, in the large degree limit, for abelian covers and infinite index congruence subgroups of SL2(Z). Résumé. — On considère ici des quotients X = ΓH2 du plan hyperbolique H2 par des groupes d’isométries convexes co-compacts Γ. On s’intéresse au comportement des résonances du Laplacien ∆X̃ où X̃ = Γ̃H2 est un revêtement Galoisien de haut degré de X. En combinant des techniques de formalisme thermodynamique et de théorie des représentations, on prouve, dans le régime de haut degré, de nouveaux théorèmes d’existence de résonances non-triviales près de l’axe {Re(s) = δ} pour deux familles de revêtements, les cas abéliens et le cas des congruences.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":"70 1","pages":"523-596"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71208585","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}
{"title":"Automorphisms of real del Pezzo surfaces and the real plane Cremona group","authors":"E. Yasinsky","doi":"10.5802/aif.3460","DOIUrl":"https://doi.org/10.5802/aif.3460","url":null,"abstract":"We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42676225","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}
{"title":"The translation number and quasi-morphisms on groups of symplectomorphisms of the disk","authors":"Shuhei Maruyama","doi":"10.5802/aif.3487","DOIUrl":"https://doi.org/10.5802/aif.3487","url":null,"abstract":"On groups of symplectomorphisms of the disk, we construct two homogeneous quasi-morphisms which relate to the Calabi invariant and the flux homomorphism respectively. We also show the relation between the quasi-morphisms and the translation number introduced by Poincar'{e}.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43249174","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}
{"title":"Coincidences of division fields","authors":"Harris B. Daniels, 'Alvaro Lozano-Robledo","doi":"10.5802/aif.3520","DOIUrl":"https://doi.org/10.5802/aif.3520","url":null,"abstract":"Let $E$ be an elliptic curve defined over $mathbb{Q}$, and let $rho_Ecolon {rm Gal}(bar{mathbb{Q}}/mathbb{Q})to {rm GL}(2,hat{mathbb{Z}})$ be the adelic representation associated to the natural action of Galois on the torsion points of $E(bar{mathbb{Q}})$. By a theorem of Serre, the image of $rho_{E}$ is open, but the image is always of index at least $2$ in ${rm GL}(2,hat{mathbb{Z}})$ due to a certain quadratic entanglement amongst division fields. In this paper, we study other types of abelian entanglements. More concretely, we classify the elliptic curves $Emathbb{Q}$, and primes $p$ and $q$ such that $mathbb{Q}(E[p])cap mathbb{Q}(zeta_{q^k})$ is non-trivial, and determine the degree of the coincidence. As a consequence, we classify all elliptic curves $E/mathbb{Q}$ and integers $m,n$ such that the $m$-th and $n$-th division fields coincide, i.e., when $mathbb{Q}(E[n])=mathbb{Q}(E[m])$.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47907649","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}
{"title":"Exotic group C * -algebras of simple Lie groups with real rank one","authors":"T. D. Laat, Timo Siebenand","doi":"10.5802/aif.3441","DOIUrl":"https://doi.org/10.5802/aif.3441","url":null,"abstract":"It is well known that the universal and the reduced group $C^*$-algebra of a locally compact group coincide if and only if the group is amenable. In general, there can be many $C^*$-algebras, called exotic group $C^*$-algebras, which lie between these two algebras. In this article, we consider simple Lie groups $G$ with real rank one and investigate their exotic group $C^{*}$-algebras $C^*_{L^{p+}}(G)$, which are defined through $L^p$-integrability properties of matrix coefficients of unitary representations of $G$. First, we show that the subset of equivalence classes of irreducible unitary $L^{p+}$-representations forms a closed ideal of the unitary dual of the groups under consideration. This result holds more generally for groups with the Kunze-Stein property. Second, for every classical simple Lie group $G$ with real rank one and every $2 leq q < p leq infty$, we determine whether the canonical quotient map $C^*_{L^{p+}}(G) twoheadrightarrow C^*_{L^{q+}}(G)$ has non-trivial kernel. To this end, it suffices to study the $L^p$-integrability properties of spherical functions of class one representations of $G$. We also obtain partial results for the exceptional Lie group $mathrm{F}_{4(-20)}$. Our results generalize, with completely different methods, recent results of Samei and Wiersma on exotic group $C^*$-algebras of $mathrm{SO}_{0}(n,1)$ and $mathrm{SU}(n,1)$. In particular, our approach also works for groups with property (T).","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46557252","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}
{"title":"A divergent horocycle in the horofunction compactification of the Teichmüller metric","authors":"Maxime Fortier Bourque","doi":"10.5802/aif.3564","DOIUrl":"https://doi.org/10.5802/aif.3564","url":null,"abstract":"We give an example of a horocycle in the Teichmuller space of the five-times-punctured sphere that does not converge in the Gardiner--Masur compactification, or equivalently in the horofunction compactification of the Teichmuller metric. As an intermediate step, we exhibit a simple closed curve whose extremal length is periodic but not constant along the horocycle. The example lifts to any Teichmuller space of complex dimension greater than one via covering constructions.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42317491","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}
{"title":"Compatibility degree of cluster complexes","authors":"Changjian Fu, Y. Gyoda","doi":"10.5802/aif.3596","DOIUrl":"https://doi.org/10.5802/aif.3596","url":null,"abstract":"We introduce a new function on the set of pairs of cluster variables via $f$-vectors, which we call it the compatibility degree (of cluster complexes). The compatibility degree is a natural generalization of the classical compatibility degree introduced by Fomin and Zelevinsky. In particular, we prove that the compatibility degree has the duality property, the symmetry property, the embedding property and the compatibility property, which the classical one has. We also conjecture that the compatibility degree has the exchangeability property. As pieces of evidence of this conjecture, we establish the exchangeability property for cluster algebras of rank 2, acyclic skew-symmetric cluster algebras, cluster algebras arising from weighted projective lines, and cluster algebras arising from marked surfaces except for the once-punctured closed surfaces.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42236208","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}
{"title":"Triangulations of non-archimedean curves, semi-stable reduction, and ramification","authors":"Lorenzo Fantini, Danièle Turchetti","doi":"10.5802/aif.3536","DOIUrl":"https://doi.org/10.5802/aif.3536","url":null,"abstract":"Let $K$ be a complete discretely valued field with algebraically closed residue field and let $mathfrak C$ be a smooth projective and geometrically connected algebraic $K$-curve of genus $g$. Assume that $ggeq 2$, so that there exists a minimal finite Galois extension $L$ of $K$ such that $mathfrak C_L$ admits a semi-stable model. In this paper, we study the extension $L|K$ in terms of the emph{minimal triangulation} of $C$, a distinguished finite subset of the Berkovich analytification $C$ of $mathfrak C$. We prove that the least common multiple $d$ of the multiplicities of the points of the minimal triangulation always divides the degree $[L:K]$. Moreover, if $d$ is prime to the residue characteristic of $K$, then we show that $d=[L:K]$, obtaining a new proof of a classical theorem of Saito. We then discuss curves with marked points, which allows us to prove analogous results in the case of elliptic curves, whose minimal triangulations we describe in full in the tame case. In the last section, we illustrate through several examples how our results explain the failure of the most natural extensions of Saito's theorem to the wildly ramified case.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46415153","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}
{"title":"Pentagon representations and complex projective structures on closed surfaces","authors":"Thomas Le Fils","doi":"10.5802/aif.3528","DOIUrl":"https://doi.org/10.5802/aif.3528","url":null,"abstract":"We define a class of representations of the fundamental group of a closed surface of genus $2$ to $mathrm{PSL}_2 (mathbb C)$: the pentagon representations. We show that they are exactly the non-elementary $mathrm{PSL}_2 (mathbb C)$-representations of surface groups that do not admit a Schottky decomposition, i.e. a pants decomposition such that the restriction of the representation to each pair of pants is an isomorphism onto a Schottky group. In doing so, we exhibit a gap in the proof of Gallo, Kapovich and Marden that every non-elementary representation of a surface group to $mathrm{PSL}_2 (mathbb C)$ is the holonomy of a projective structure, possibly with one branched point of order $2$. We show that pentagon representations arise as such holonomies and repair their proof.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46426516","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}