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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 4 Cover and Front matter
• PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748020000304
Issue No: Vol. 19, No. 4 (2020)

• JMJ volume 19 Issue 4 Cover and Back matter
• PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748020000316
Issue No: Vol. 19, No. 4 (2020)

• CHABAUTY LIMITS OF ALGEBRAIC GROUPS ACTING ON TREES THE QUASI-SPLIT CASE
• Authors: Thierry Stulemeijer
Pages: 1031 - 1091
Abstract: Given a locally finite leafless tree $T$ , various algebraic groups over local fields might appear as closed subgroups of $\operatorname{Aut}(T)$ . We show that the set of closed cocompact subgroups of $\operatorname{Aut}(T)$ that are isomorphic to a quasi-split simple algebraic group is a closed subset of the Chabauty space of $\operatorname{Aut}(T)$ . This is done via a study of the integral Bruhat–Tits model of $\operatorname{SL}_{2}$ and $\operatorname{SU}_{3}^{L/K}$ , that we carry on over arbitrary local fields, without any restriction on the (residue) characteristic. In particular, we show that in residue characteristic $2$ , the Tits index of simple algebraic subgroups of $\operatorname{Aut}(T)$ is not always preserved under Chabauty limits.
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000282
Issue No: Vol. 19, No. 4 (2020)

• CHABAUTY LIMITS OF SIMPLE GROUPS ACTING ON TREES
• Authors: Pierre-Emmanuel Caprace; Nicolas Radu
Pages: 1093 - 1120
Abstract: Let $T$ be a locally finite tree without vertices of degree  $1$ . We show that among the closed subgroups of $\text{Aut}(T)$ acting with a bounded number of orbits, the Chabauty-closure of the set of topologically simple groups is the set of groups without proper open subgroup of finite index. Moreover, if all vertices of $T$ have degree ${\geqslant}3$ , then the set of isomorphism classes of topologically simple closed subgroups of $\text{Aut}(T)$ acting doubly transitively on $\unicode[STIX]{x2202}T$ carries a natural compact Hausdorff topology inherited from Chabauty. Some of our considerations are valid in the context of automorphism groups of locally finite connected graphs. Applications to Weyl-transitive automorphism groups of buildings are also presented.
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000348
Issue No: Vol. 19, No. 4 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\text{II}_{1}$ ++++++++++++ ++++++++ +++++FACTORS&rft.title=Journal+of+the+Institute+of+Mathematics+of+Jussieu&rft.issn=1474-7480&rft.date=2020&rft.volume=19&rft.spage=1121&rft.epage=1139&rft.aulast=Isono&rft.aufirst=Yusuke&rft.au=Yusuke+Isono&rft_id=info:doi/10.1017/S1474748018000336">ON FUNDAMENTAL GROUPS OF TENSOR PRODUCT $\text{II}_{1}$ FACTORS
• Authors: Yusuke Isono
Pages: 1121 - 1139
Abstract: Let $M$ be a $\text{II}_{1}$ factor and let ${\mathcal{F}}(M)$ denote the fundamental group of $M$ . In this article, we study the following property of $M$ : for any $\text{II}_{1}$ factor $B$ , we have ${\mathcal{F}}(M\,\overline{\otimes }\,B)={\mathcal{F}}(M){\mathcal{F}}(B)$ . We prove that for any subgroup $G\leqslant \mathbb{R}_{+}^{\ast }$ which is realized as a fundamental group of a $\text{II}_{1}$ factor, there exists a $\text{II}_{1}$ factor
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000336
Issue No: Vol. 19, No. 4 (2020)

• DEGENERATION OF ENDOMORPHISMS OF THE COMPLEX PROJECTIVE SPACE IN THE
HYBRID SPACE
• Authors: Charles Favre
Pages: 1141 - 1183
Abstract: We consider a meromorphic family of endomorphisms of degree at least 2 of a complex projective space that is parameterized by the unit disk. We prove that the measure of maximal entropy of these endomorphisms converges to the equilibrium measure of the associated non-Archimedean dynamical system when the system degenerates. The convergence holds in the hybrid space constructed by Berkovich and further studied by Boucksom and Jonsson. We also infer from our analysis an estimate for the blow-up of the Lyapunov exponent near a pole in one-dimensional families of endomorphisms.
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S147474801800035X
Issue No: Vol. 19, No. 4 (2020)

• MICROLOCAL REGULARITY FOR MIZOHATA TYPE DIFFERENTIAL OPERATORS
• Authors: G. Hoepfner; R. Medrado
Pages: 1185 - 1209
Abstract: We investigate interesting connections between Mizohata type vector fields and microlocal regularity of nonlinear first-order PDEs, establishing results in Denjoy–Carleman classes and real analyticity results in the linear case.
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000361
Issue No: Vol. 19, No. 4 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$(G,\unicode[STIX]{x1D707})$ ++++++++++++ ++++++++ ++++-DISPLAYS+AND+RAPOPORT–ZINK+SPACES&rft.title=Journal+of+the+Institute+of+Mathematics+of+Jussieu&rft.issn=1474-7480&rft.date=2020&rft.volume=19&rft.spage=1211&rft.epage=1257&rft.aulast=Bültel&rft.aufirst=O.&rft.au=O.+Bültel&rft.au=G.+Pappas&rft_id=info:doi/10.1017/S1474748018000373">$(G,\unicode[STIX]{x1D707})$ -DISPLAYS AND RAPOPORT–ZINK SPACES
• Authors: O. Bültel; G. Pappas
Pages: 1211 - 1257
Abstract: Let $(G,\unicode[STIX]{x1D707})$ be a pair of a reductive group $G$ over the $p$ -adic integers and a minuscule cocharacter $\unicode[STIX]{x1D707}$ of $G$ defined over an unramified extension. We introduce and study ‘ $(G,\unicode[STIX]{x1D707})$ -displays’ which generalize Zink’s Witt vector displays. We use these to define certain Rapoport–Zink formal schemes purely group theoretically, i.e. without $p$ -divisible groups.
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000373
Issue No: Vol. 19, No. 4 (2020)

• ON THE DISTRIBUTION OF THE MAXIMUM OF CUBIC EXPONENTIAL SUMS
• Authors: Youness Lamzouri
Pages: 1259 - 1286
Abstract: In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as ‘Birch sums’. Our main theorem gives upper and lower bounds (of nearly the same order of magnitude) for the distribution of large values of this maximum, that hold in a wide uniform range. This improves a recent result of Kowalski and Sawin. The proofs use a blend of probabilistic methods, harmonic analysis techniques, and deep tools from algebraic geometry. The results can also be generalized to other types of $\ell$ -adic trace functions. In particular, the lower bound of our result also holds for partial sums of Kloosterman sums. As an application, we show that there exist $x\in [1,p]$ and $a\in \mathbb{F}_{p}^{\times }$ such that $|\sum _{n\leqslant x}\exp (2\unicode[STIX]{x1D70B}i(n^{3}+an)/p)|\geqslant (2/\unicode[STIX]{x1D70B}+o(1))\sqrt{p}\log \log p$ . The uniformity of our results suggests that this bound is optimal, up to the value of the constant.
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000385
Issue No: Vol. 19, No. 4 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$p$ ++++++++++++ ++++++++ ++++-ADIC+ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$L$ ++++++++++++ ++++++++ ++++-FUNCTIONS+FOR+ORDINARY+FAMILIES+ON+SYMPLECTIC+GROUPS&rft.title=Journal+of+the+Institute+of+Mathematics+of+Jussieu&rft.issn=1474-7480&rft.date=2020&rft.volume=19&rft.spage=1287&rft.epage=1347&rft.aulast=Liu&rft.aufirst=Zheng&rft.au=Zheng+Liu&rft_id=info:doi/10.1017/S1474748018000415">$p$ -ADIC $L$ -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS
• Authors: Zheng Liu
Pages: 1287 - 1347
Abstract: We construct the $p$ -adic standard $L$ -functions for ordinary families of Hecke eigensystems of the symplectic group $\operatorname{Sp}(2n)_{/\mathbb{Q}}$ using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group $\operatorname{Sp}(4n)_{/\mathbb{Q}}$ , which guarantees the nonvanishing of local zeta integrals and allows us to $p$ -adically interpolate the restrictions of the Siegel Eisenstein series to $\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$ .
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000415
Issue No: Vol. 19, No. 4 (2020)

• BEYOND ENDOSCOPY VIA THE TRACE FORMULA – III THE STANDARD
REPRESENTATION
• Authors: S. Ali Altuğ
Pages: 1349 - 1387
Abstract: We finalize the analysis of the trace formula initiated in S. A. Altuğ [Beyond endoscopy via the trace formula-I: Poisson summation and isolation of special representations, Compos. Math.151(10) (2015), 1791–1820] and developed in S. A. Altuğ [Beyond endoscopy via the trace formula-II: asymptotic expansions of Fourier transforms and bounds toward the Ramanujan conjecture. Submitted, preprint, 2015, Available at: arXiv:1506.08911.pdf], and calculate the asymptotic expansion of the beyond endoscopic averages for the standard $L$ -functions attached to weight $k\geqslant 3$ cusp forms on $\mathit{GL}(2)$ (cf. Theorem 1.1). This, in particular, constitutes the first example of beyond endoscopy executed via the Arthur–Selberg trace formula, as originally proposed in R. P. Langlands [Beyond endoscopy, in Contributions to Automorphic Forms, Geometry, and Number Theory, pp. 611–698 (The Johns Hopkins University Press, Baltimore, MD, 2004), chapter 22]. As an application we also give a new proof of the analytic continuation of the $L$ -function attached to Ramanujan’s $\unicode[STIX]{x1D6E5}$ -function.
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000427
Issue No: Vol. 19, No. 4 (2020)

• FUJITA DECOMPOSITION AND HODGE LOCI
• Authors: Paola Frediani; Alessandro Ghigi, Gian Pietro Pirola
Pages: 1389 - 1408
Abstract: This paper contains two results on Hodge loci in $\mathsf{M}_{g}$ . The first concerns fibrations over curves with a non-trivial flat part in the Fujita decomposition. If local Torelli theorem holds for the fibers and the fibration is non-trivial, an appropriate exterior power of the cohomology of the fiber admits a Hodge substructure. In the case of curves it follows that the moduli image of the fiber is contained in a proper Hodge locus. The second result deals with divisors in $\mathsf{M}_{g}$ . It is proved that the image under the period map of a divisor in $\mathsf{M}_{g}$ is not contained in a proper totally geodesic subvariety of $\mathsf{A}_{g}$ . It follows that a Hodge locus in $\mathsf{M}_{g}$ has codimension at least 2.
PubDate: 2020-07-01T00:00:00.000Z
DOI: 10.1017/S1474748018000452
Issue No: Vol. 19, No. 4 (2020)

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