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Journal of the Institute of Mathematics of Jussieu
Journal Prestige (SJR): 2.393  Citation Impact (citeScore): 1 Number of Followers: 0  Hybrid journal (It can contain Open Access articles)ISSN (Print) 1474-7480 - ISSN (Online) 1475-3030 Published by Cambridge University Press  [389 journals]
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- JMJ volume 19 Issue 6 Cover and Front matter
- PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748020000341
Issue No: Vol. 19, No. 6 (2020)
- PubDate: 2020-11-01T00:00:00.000Z
- JMJ volume 19 Issue 6 Cover and Back matter
- PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748020000353
Issue No: Vol. 19, No. 6 (2020)
- PubDate: 2020-11-01T00:00:00.000Z
- ANALOGUES OF CENTRALIZER SUBALGEBRAS FOR FIAT 2-CATEGORIES AND THEIR
2-REPRESENTATIONS- Authors: Marco Mackaay; Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang
Pages: 1793 - 1829
Abstract: The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex
${\mathcal{J}}$ of a fiat 2-category 
$\mathscr{C}$ and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of 
$\mathscr{C}$ associated with a diagonal 
${\mathcal{H}}$ -cell in 
${\mathcal{J}}$ . As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types 
$B_{3}$ and 
$B_{4}$ .
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748018000555
Issue No: Vol. 19, No. 6 (2020)
- Authors: Marco Mackaay; Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang
- LARGE-SCALE SUBLINEARLY LIPSCHITZ GEOMETRY OF HYPERBOLIC SPACES
- Authors: Gabriel Pallier
Pages: 1831 - 1876
Abstract: Large-scale sublinearly Lipschitz maps have been introduced by Yves Cornulier in order to precisely state his theorems about asymptotic cones of Lie groups. In particular, Sublinearly bi-Lipschitz Equivalences (SBE) are a weak variant of quasi-isometries, with the only requirement of still inducing bi-Lipschitz maps at the level of asymptotic cones. We focus here on hyperbolic metric spaces and study properties of boundary extensions of SBEs, reminiscent of quasi-Möbius (or quasisymmetric) mappings. We give a dimensional invariant of the boundary that allows to distinguish hyperbolic symmetric spaces up to SBE, answering a question of Druţu.
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748018000567
Issue No: Vol. 19, No. 6 (2020)
- Authors: Gabriel Pallier
- ANALYTIC HYPOELLIPTICITY FOR SUMS OF SQUARES IN THE PRESENCE OF SYMPLECTIC
NON TREVES STRATA- Authors: Antonio Bove; Marco Mughetti
Pages: 1877 - 1888
Abstract: In Albano, Bove and Mughetti [J. Funct. Anal. 274(10) (2018), 2725–2753]; Bove and Mughetti [Anal. PDE 10(7) (2017), 1613–1635] it was shown that Treves conjecture for the real analytic hypoellipticity of sums of squares operators does not hold. Models were proposed where the critical points causing a non-analytic regularity might be interpreted as strata. We stress that up to now there is no notion of stratum which could replace the original Treves stratum. In the proposed models such ‘strata’ were non-symplectic analytic submanifolds of the characteristic variety. In this note we modify one of those models in such a way that the critical points are a symplectic submanifold of the characteristic variety while still not being a Treves stratum. We show that the operator is analytic hypoelliptic.
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748018000580
Issue No: Vol. 19, No. 6 (2020)
- Authors: Antonio Bove; Marco Mughetti
- PARABOLIC KAZHDAN–LUSZTIG BASIS, SCHUBERT CLASSES, AND EQUIVARIANT
ORIENTED COHOMOLOGY- Authors: Cristian Lenart; Kirill Zainoulline, Changlong Zhong
Pages: 1889 - 1929
Abstract: We study the equivariant oriented cohomology ring
$\mathtt{h}_{T}(G/P)$ of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and then prove that the respective Bott–Samelson classes in 
$\mathtt{h}_{T}(G/P)$ can be obtained by applying this action to the fundamental class of the identity point, hence generalizing previously known results of Chow groups by Brion, Knutson, Peterson, Tymoczko and others. Our main result concerns the equivariant oriented cohomology theory 
$\mathfrak{h}$ corresponding to the 2-parameter Todd genus. We give a new interpretation of Deodhar’s parabolic Kazhdan–Lusztig basis, i.e., we realize it as some cohomology classes (the parabolic Kazhdan–Lusztig (KL) Schubert classes) in 
$\mathfrak{h}_{T}(G/P)$ . We make a positivity conjecture, and a conjecture about the relationship of such classes with smoothness of Schubert varieties. We also prove the latter in several special cases.
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748018000592
Issue No: Vol. 19, No. 6 (2020)
- Authors: Cristian Lenart; Kirill Zainoulline, Changlong Zhong
- TOWARDS A NON-ARCHIMEDEAN ANALYTIC ANALOG OF THE BASS–QUILLEN
CONJECTURE- Authors: Moritz Kerz; Shuji Saito, Georg Tamme
Pages: 1931 - 1946
Abstract: We suggest an analog of the Bass–Quillen conjecture for smooth affinoid algebras over a complete non-archimedean field. We prove this in the rank-1 case, i.e. for the Picard group. For complete discretely valued fields and regular affinoid algebras that admit a regular model (automatic if the residue characteristic is zero) we prove a similar statement for the Grothendieck group of vector bundles
$K_{0}$ .
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S147474801900001X
Issue No: Vol. 19, No. 6 (2020)
- Authors: Moritz Kerz; Shuji Saito, Georg Tamme
HIRZEBRUCH–ZAGIER CYCLES- Authors: Iván Blanco-Chacón; Michele Fornea
Pages: 1947 - 1992
Abstract: Let
$L/F$ be a quadratic extension of totally real number fields. For any prime 
$p$ unramified in 
$L$ , we construct a 
$p$ -adic 
$L$ -function interpolating the central values of the twisted triple product 
$L$ -functions attached to a 
$p$ -nearly ordinary family of unitary cuspidal automorphic representations of 
$\text{Res}_{L\times F/F}(\text{GL}_{2})$ . Furthermore, when 
$L/\mathbb{Q}$ is a real quadratic number field and 
$p$ is a split prime, we prove a 
$p$ -adic Gross–Zagier formula relating the values of the
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748019000021
Issue No: Vol. 19, No. 6 (2020)
- Authors: Iván Blanco-Chacón; Michele Fornea
- HIGHER ORDER DIFFERENTIABILITY OF OPERATOR FUNCTIONS IN SCHATTEN NORMS
- Authors: Christian Le Merdy; Anna Skripka
Pages: 1993 - 2016
Abstract: We establish the following results on higher order
${\mathcal{S}}^{p}$ -differentiability, 
$1
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748019000033
Issue No: Vol. 19, No. 6 (2020)
- Authors: Christian Le Merdy; Anna Skripka
OF $\text{GL}(n)$ AND THE LOCAL JACQUET–LANGLANDS CORRESPONDENCE- Authors: Yoichi Mieda
Pages: 2017 - 2043
Abstract: We determine the parity of the Langlands parameter of a conjugate self-dual supercuspidal representation of
$\text{GL}(n)$ over a non-archimedean local field by means of the local Jacquet–Langlands correspondence. It gives a partial generalization of a previous result on the self-dual case by Prasad and Ramakrishnan.
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748019000045
Issue No: Vol. 19, No. 6 (2020)
- Authors: Yoichi Mieda
- WEIERSTRASS PRYM EIGENFORMS IN GENUS FOUR
- Authors: Erwan Lanneau; Duc-Manh Nguyen
Pages: 2045 - 2085
Abstract: We prove the connectedness of the Prym eigenforms loci in genus four (for real multiplication by some order of discriminant
$D$ ), for any 
$D$ . These loci were discovered by McMullen in 2006.
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748019000057
Issue No: Vol. 19, No. 6 (2020)
- Authors: Erwan Lanneau; Duc-Manh Nguyen
- LINEAR SYSTEMS ON IRREGULAR VARIETIES
- Authors: Miguel Ángel Barja; Rita Pardini, Lidia Stoppino
Pages: 2087 - 2125
Abstract: Let
$X$ be a normal complex projective variety, 
$T\subseteq X$ a subvariety of dimension 
$m$ (possibly 
$T=X$ ) and 
$a:X\rightarrow A$ a morphism to an abelian variety such that 
$\text{Pic}^{0}(A)$ injects into 
$\text{Pic}^{0}(T)$ ; let 
$L$ be a line bundle on 
$X$ and 
$\unicode[STIX]{x1D6FC}\in \text{Pic}^{0}(A)$ a general element.We introduce two new ingredients for the study of linear systems on 
$X$ . First of all, we show the existence of a factorization of the map
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748019000069
Issue No: Vol. 19, No. 6 (2020)
- Authors: Miguel Ángel Barja; Rita Pardini, Lidia Stoppino
- Authors: Francesc Castella
Pages: 2127 - 2164
Abstract: In this paper, we prove an ‘explicit reciprocity law’ relating Howard’s system of big Heegner points to a two-variable
$p$ -adic 
$L$ -function (constructed here) interpolating the 
$p$ -adic Rankin 
$L$ -series of Bertolini–Darmon–Prasanna in Hida families. As applications, we obtain a direct relation between classical Heegner cycles and the higher weight specializations of big Heegner points, refining earlier work of the author, and prove the vanishing of Selmer groups of CM elliptic curves twisted by 2-dimensional Artin representations in cases predicted by the equivariant Birch and Swinnerton-Dyer conjecture.
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748019000094
Issue No: Vol. 19, No. 6 (2020)
- Authors: Francesc Castella
- THE KUGA–SATAKE CONSTRUCTION UNDER DEGENERATION
- Authors: Stefan Schreieder; Andrey Soldatenkov
Pages: 2165 - 2182
Abstract: We extend the Kuga–Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga–Satake abelian varieties associated with polarized variations of K3 type Hodge structures over the punctured disc.
PubDate: 2020-11-01T00:00:00.000Z
DOI: 10.1017/S1474748019000239
Issue No: Vol. 19, No. 6 (2020)
- Authors: Stefan Schreieder; Andrey Soldatenkov
