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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  [374 journals]
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- JMJ volume 18 Issue 5 Cover and Front matter
- PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748019000446
Issue No: Vol. 18, No. 5 (2019)
- PubDate: 2019-09-01T00:00:00.000Z
- JMJ volume 18 Issue 5 Cover and Back matter
- PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748019000458
Issue No: Vol. 18, No. 5 (2019)
- PubDate: 2019-09-01T00:00:00.000Z
- A CATEGORIFICATION OF A QUANTUM FROBENIUS MAP
- Authors: You Qi
Pages: 899 - 939
Abstract: A quantum Frobenius map a la Lusztig for
$\mathfrak{s}\mathfrak{l}_{2}$ is categorified at a prime root of unity.
PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748017000275
Issue No: Vol. 18, No. 5 (2019)
- Authors: You Qi
- CM RELATIONS IN FIBERED POWERS OF ELLIPTIC FAMILIES
- Authors: Fabrizio Barroero
Pages: 941 - 956
Abstract: Let
$E_{\unicode[STIX]{x1D706}}$ be the Legendre family of elliptic curves. Given 
$n$ points 
$P_{1},\ldots ,P_{n}\in E_{\unicode[STIX]{x1D706}}(\overline{\mathbb{Q}(\unicode[STIX]{x1D706})})$ , linearly independent over 
$\mathbb{Z}$ , we prove that there are at most finitely many complex numbers 
$\unicode[STIX]{x1D706}_{0}$ such that 
$E_{\unicode[STIX]{x1D706}_{0}}$ has complex multiplication and 
$P_{1}(\unicode[STIX]{x1D706}_{0}),\ldots ,P_{n}(\unicode[STIX]{x1D706}_{0})$ are linearly dependent over End
$(E_{\unicode[STIX]{x1D706}_{0}})$ . This implies a positive answer to a question of Bertrand and, combined with a previous work in collaboration with Capuano, proves the Zilber–Pink conjecture for a curve in a fibered power of an elliptic scheme when everything is defined over 
$\overline{\mathbb{Q}}$ .
PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748017000287
Issue No: Vol. 18, No. 5 (2019)
- Authors: Fabrizio Barroero
- Authors: Daniel Caro
Pages: 957 - 991
Abstract: In the framework of Berthelot’s theory of arithmetic
${\mathcal{D}}$ -modules, we prove the 
$p$ -adic analogue of Betti number estimates and we give some standard applications.
PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748017000299
Issue No: Vol. 18, No. 5 (2019)
- Authors: Daniel Caro
- A VARIANT OF HARISH-CHANDRA FUNCTORS
- Authors: Tyrone Crisp; Ehud Meir, Uri Onn
Pages: 993 - 1049
Abstract: Harish-Chandra induction and restriction functors play a key role in the representation theory of reductive groups over finite fields. In this paper, extending earlier work of Dat, we introduce and study generalisations of these functors which apply to a wide range of finite and profinite groups, typical examples being compact open subgroups of reductive groups over non-archimedean local fields. We prove that these generalisations are compatible with two of the tools commonly used to study the (smooth, complex) representations of such groups, namely Clifford theory and the orbit method. As a test case, we examine in detail the induction and restriction of representations from and to the Siegel Levi subgroup of the symplectic group
$\text{Sp}_{4}$ over a finite local principal ideal ring of length two. We obtain in this case a Mackey-type formula for the composition of these induction and restriction functors which is a perfect analogue of the well-known formula for the composition of Harish-Chandra functors. In a different direction, we study representations of the Iwahori subgroup 
$I_{n}$ of 
$\text{GL}_{n}(F)$ , where 
$F$ is a non-archimedean local field. We establish a bijection between the set of irreducible representations of 
$I_{n}$ and tuples of primitive irreducible representations of smaller Iwahori subgroups, where primitivity is defined by the vanishing of suitable restriction functors.
PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748017000305
Issue No: Vol. 18, No. 5 (2019)
- Authors: Tyrone Crisp; Ehud Meir, Uri Onn
- Authors: Amalendu Krishna; Husney Parvez Sarwar
Pages: 1051 - 1085
Abstract: We show that for any commutative Noetherian regular ring
$R$ containing 
$\mathbb{Q}$ , the map 
$K_{1}(R)\rightarrow K_{1}\left(\frac{R[x_{1},\ldots ,x_{4}]}{(x_{1}x_{2}-x_{3}x_{4})}\right)$ is an isomorphism. This answers a question of Gubeladze. We also compute the higher 
$K$ -theory of this monoid algebra. In particular, we show that the above isomorphism does not extend to all higher 
$K$ -groups. We give applications to a question of Lindel on the Serre dimension of monoid algebras.
PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748017000317
Issue No: Vol. 18, No. 5 (2019)
- Authors: Amalendu Krishna; Husney Parvez Sarwar
- ONE POSITIVE AND TWO NEGATIVE RESULTS FOR DERIVED CATEGORIES OF ALGEBRAIC
STACKS- Authors: Jack Hall; Amnon Neeman, David Rydh
Pages: 1087 - 1111
Abstract: Let
$X$ be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of 
$X$ : (1) 
$\mathsf{D}_{\text{qc}}(X)$ is compactly generated by perfect complexes and (2) if 
$X$ is noetherian or has affine diagonal, then the functor 
$\unicode[STIX]{x1D6F9}_{X}:\mathsf{D}(\mathsf{QCoh}(X))\rightarrow \mathsf{D}_{\text{qc}}(X)$ is an equivalence. Our main results are that for algebraic stacks in positive characteristic, the assertions (1) and (2) are typically false.
PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748017000366
Issue No: Vol. 18, No. 5 (2019)
- Authors: Jack Hall; Amnon Neeman, David Rydh
- SYMMETRIC OPERADS IN ABSTRACT SYMMETRIC SPECTRA – ERRATUM
- Authors: Dmitri Pavlov; Jakob Scholbach
Pages: 1113 - 1113
PubDate: 2019-09-01T00:00:00.000Z
DOI: 10.1017/S1474748019000379
Issue No: Vol. 18, No. 5 (2019)
- Authors: Dmitri Pavlov; Jakob Scholbach
