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Similar Journals
 Journal of the Institute of Mathematics of JussieuJournal Prestige (SJR): 2.393 Citation Impact (citeScore): 1Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1474-7480 - ISSN (Online) 1475-3030 Published by Cambridge University Press  [387 journals]
• JMJ volume 19 Issue 5 Cover and Front matter
• PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748020000328
Issue No: Vol. 19, No. 5 (2020)

• JMJ volume 19 Issue 5 Cover and Back matter
• PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S147474802000033X
Issue No: Vol. 19, No. 5 (2020)

• SPECTRAL ANALYSIS OF MORSE–SMALE FLOWS I: CONSTRUCTION OF THE
ANISOTROPIC SPACES
• Authors: Nguyen Viet Dang; Gabriel Rivière
Pages: 1409 - 1465
Abstract: We prove the existence of a discrete correlation spectrum for Morse–Smale flows acting on smooth forms on a compact manifold. This is done by constructing spaces of currents with anisotropic Sobolev regularity on which the Lie derivative has a discrete spectrum.
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000439
Issue No: Vol. 19, No. 5 (2020)

• ZERO-LOCI OF BRAUER GROUP ELEMENTS ON SEMI-SIMPLE ALGEBRAIC GROUPS
• Authors: Daniel Loughran; Ramin Takloo-Bighash, Sho Tanimoto
Pages: 1467 - 1507
Abstract: We consider the problem of counting the number of rational points of bounded height in the zero-loci of Brauer group elements on semi-simple algebraic groups over number fields. We obtain asymptotic formulae for the counting problem for wonderful compactifications using the spectral theory of automorphic forms. Applications include asymptotic formulae for the number of matrices over $\mathbb{Q}$ whose determinant is a sum of two squares. These results provide a positive answer to some cases of a question of Serre concerning such counting problems.
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000440
Issue No: Vol. 19, No. 5 (2020)

• A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN
GENERAL POSITION
• Authors: Ziv Ran
Pages: 1509 - 1519
Abstract: We consider compact Kählerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic holomorphic Poisson structure $\unicode[STIX]{x1D6F1}$ which is sufficiently general, in a precise linear sense, with respect to its (normal-crossing) degeneracy divisor $D(\unicode[STIX]{x1D6F1})$ . We prove that $(X,\unicode[STIX]{x1D6F1})$ has unobstructed deformations, that the tangent space to its deformation space can be identified in terms of the mixed Hodge structure on $H^{2}$ of the open symplectic manifold $X\setminus D(\unicode[STIX]{x1D6F1})$ , and in fact coincides with this $H^{2}$ provided the Hodge number $h_{X}^{2,0}=0$ , and finally that the degeneracy locus $D(\unicode[STIX]{x1D6F1})$ deforms locally trivially under deformations of $(X,\unicode[STIX]{x1D6F1})$ .
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000464
Issue No: Vol. 19, No. 5 (2020)

• SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS
• Authors: Haruzo Hida; Jacques Tilouine
Pages: 1521 - 1572
Abstract: We prove, under some assumptions, a Greenberg type equality relating the characteristic power series of the Selmer groups over $\mathbb{Q}$ of higher symmetric powers of the Galois representation associated to a Hida family and congruence ideals associated to (different) higher symmetric powers of that Hida family. We use $R=T$ theorems and a sort of induction based on branching laws for adjoint representations. This method also applies to other Langlands transfers, like the transfer from $\text{GSp}(4)$ to $U(4)$ . In that case we obtain a corollary for abelian surfaces.
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000476
Issue No: Vol. 19, No. 5 (2020)

• RECOVERY OF NON-COMPACTLY SUPPORTED COEFFICIENTS OF ELLIPTIC EQUATIONS ON
AN INFINITE WAVEGUIDE
• Authors: Yavar Kian
Pages: 1573 - 1600
Abstract: We consider the unique recovery of a non-compactly supported and non-periodic perturbation of a Schrödinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery of a general class of electric potentials from the partial Dirichlet-to-Neumann map, where the Dirichlet data is supported on slightly more than half of the boundary and the Neumann data is taken on the other half of the boundary. We apply this result in different contexts including recovery of some general class of non-compactly supported coefficients from measurements on a bounded subset and recovery of an electric potential, supported on an unbounded cylinder, of a Schrödinger operator in a slab.
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000488
Issue No: Vol. 19, No. 5 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$K3$ ++++++++++++ ++++++++ +++++CATEGORIES,+ONE-CYCLES+ON+CUBIC+FOURFOLDS,+AND+THE+BEAUVILLE–VOISIN+FILTRATION&rft.title=Journal+of+the+Institute+of+Mathematics+of+Jussieu&rft.issn=1474-7480&rft.date=2020&rft.volume=19&rft.spage=1601&rft.epage=1627&rft.aulast=Shen&rft.aufirst=Junliang&rft.au=Junliang+Shen&rft.au=Qizheng+Yin&rft_id=info:doi/10.1017/S147474801800049X">$K3$ CATEGORIES, ONE-CYCLES ON CUBIC FOURFOLDS, AND THE BEAUVILLE–VOISIN
FILTRATION
• Authors: Junliang Shen; Qizheng Yin
Pages: 1601 - 1627
Abstract: We explore the connection between $K3$ categories and 0-cycles on holomorphic symplectic varieties. In this paper, we focus on Kuznetsov’s noncommutative $K3$ category associated to a nonsingular cubic 4-fold.By introducing a filtration on the $\text{CH}_{1}$ -group of a cubic 4-fold $Y$ , we conjecture a sheaf/cycle correspondence for the associated $K3$ category  ${\mathcal{A}}_{Y}$ . This is a noncommutative analog of O’Grady’s conjecture concerning derived categories of $K3$ surfaces. We study instances of our conjecture involving rational curves in cubic 4-folds, and verify the conjecture for sheaves supported on low degree rational curves.Our method provides systematic constructions of (a) the Beauville–Voisin filtration on the $\text{CH}_{0}$ -group and (b) algebraically coisotropic subvarieties of a holomorphic symplectic variety which is a moduli space of stable objects in ${\mathcal{A}}_{Y}$ .
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S147474801800049X
Issue No: Vol. 19, No. 5 (2020)

• WKB EXPANSIONS FOR HYPERBOLIC BOUNDARY VALUE PROBLEMS IN A STRIP:
SELFINTERACTION MEETS STRONG WELL-POSEDNESS
• Authors: Antoine Benoit
Pages: 1629 - 1675
Abstract: In this article we are interested in the rigorous construction of WKB expansions for hyperbolic boundary value problems in the strip $\mathbb{R}^{d-1}\times [0,1]$ . In this geometry, a new inversibility condition has to be imposed to construct the WKB expansion. This new condition is due to selfinteraction phenomenon which naturally appear when several boundary conditions are imposed. More precisely, by selfinteraction we mean that some rays can regenerated themselves after some rebounds against the sides of the strip. This phenomenon is not new and has already been studied in Benoit (Geometric optics expansions for hyperbolic corner problems, I: self-interaction phenomenon, Anal. PDE9(6) (2016), 1359–1418), Sarason and Smoller (Geometrical optics and the corner problem, Arch. Rat. Mech. Anal.56 (1974/75), 34–69) in the corner geometry. In this framework the existence of such selfinteracting rays is linked to specific geometries of the characteristic variety and may seem to be somewhat anecdotal. However for the strip geometry such rays become generic. The new inversibility condition, used to construct the WKB expansion, is a microlocalized version of the one characterizing the uniform in time strong well-posedness (Benoit, Lower exponential strong well-posedness of hyperbolic boundary value problems in a strip (preprint)). It is interesting to point here that such a situation already occurs in the half space geometry (Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math.23 (1970), 277–298).
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000506
Issue No: Vol. 19, No. 5 (2020)

• ON TYPICALITY OF TRANSLATION FLOWS WHICH ARE DISJOINT WITH THEIR INVERSE
• Authors: Przemysław Berk; Krzysztof Frączek, Thierry de la Rue
Pages: 1677 - 1737
Abstract: In this paper we prove that the set of translation structures for which the corresponding vertical translation flows are disjoint with its inverse contains a $G_{\unicode[STIX]{x1D6FF}}$ -dense subset in every non-hyperelliptic connected component of the moduli space ${\mathcal{M}}$ . This is in contrast to hyperelliptic case, where for every translation structure the associated vertical flow is reversible, i.e., it is isomorphic to its inverse by an involution. To prove the main result, we study limits of the off-diagonal 3-joinings of special representations of vertical translation flows. Moreover, we construct a locally defined continuous embedding of the moduli space into the space of measure-preserving flows to obtain the $G_{\unicode[STIX]{x1D6FF}}$ -condition. Moreover, as a by-product we get that in every non-hyperelliptic connected component of the moduli space there is a dense subset of translation structures whose vertical flow is reversible.
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000531
Issue No: Vol. 19, No. 5 (2020)

• CATEGORICAL PROOF OF HOLOMORPHIC ATIYAH–BOTT FORMULA
• Authors: Grigory Kondyrev; Artem Prikhodko
Pages: 1739 - 1763
Abstract: Given a $2$ -commutative diagramin a symmetric monoidal $(\infty ,2)$ -category $\mathscr{E}$ where $X,Y\in \mathscr{E}$ are dualizable objects and $\unicode[STIX]{x1D711}$ admits a right adjoint we construct a natural morphism $\mathsf{Tr}_{\mathscr{E}}(F_{X})\xrightarrow[{}]{~~~~~}\mathsf{Tr}_{\mathscr{E}}(F_{Y})$ between the traces of $F_{X}$ and $F_{Y}$ , respectively. We then apply this formalism to the case when $\mathscr{E}$ is the $(\infty ,2)$ -category of $k$ ...
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000543
Issue No: Vol. 19, No. 5 (2020)

• NON-HYPERBOLIC ERGODIC MEASURES AND HORSESHOES IN PARTIALLY HYPERBOLIC
HOMOCLINIC CLASSES
• Authors: Dawei Yang; Jinhua Zhang
Pages: 1765 - 1792
Abstract: We study a rich family of robustly non-hyperbolic transitive diffeomorphisms and we show that each ergodic measure is approached by hyperbolic sets in weak $\ast$ -topology and in entropy. For hyperbolic ergodic measures, it is a classical result of A. Katok. The novelty here is to deal with non-hyperbolic ergodic measures. As a consequence, we obtain the continuity of topological entropy.
PubDate: 2020-09-01T00:00:00.000Z
DOI: 10.1017/S1474748018000579
Issue No: Vol. 19, No. 5 (2020)

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