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  • Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups
    Can. J. Math. (IF 0.830) Pub Date : 2019-01-09
    Pramod N. Achar; Simon Riche; Cristian Vay

    In this paper we construct an abelian category of mixed perverse sheaves attached to any realization of a Coxeter group, in terms of the associated Elias–Williamson diagrammatic category. This construction extends previous work of the first two authors, where we worked with parity complexes instead of diagrams, and we extend most of the properties known in this case to the general setting. As an application we prove that the split Grothendieck group of the Elias–Williamson diagrammatic category is isomorphic to the corresponding Hecke algebra, for any choice of realization.

    更新日期:2020-01-04
  • Ramification of the Eigencurve at Classical RM Points
    Can. J. Math. (IF 0.830) Pub Date : 2019-03-07
    Adel Betina

    J. Bellaïche and M. Dimitrov showed that the $p$ -adic eigencurve is smooth but not étale over the weight space at $p$ -regular theta series attached to a character of a real quadratic field $F$ in which $p$ splits. In this paper we prove the existence of an isomorphism between the subring fixed by the Atkin–Lehner involution of the completed local ring of the eigencurve at these points and a universal ring representing a pseudo-deformation problem. Additionally, we give a precise criterion for which the ramification index is exactly 2. We finish this paper by proving the smoothness of the nearly ordinary and ordinary Hecke algebras for Hilbert modular forms over $F$ at the overconvergent cuspidal Eisenstein points, being the base change lift for $\text{GL}(2)_{/F}$ of these theta series. Our approach uses deformations and pseudo-deformations of reducible Galois representations.

    更新日期:2020-01-04
  • Bakry–Émery Curvature Functions on Graphs
    Can. J. Math. (IF 0.830) Pub Date : 2019-01-07
    David Cushing; Shiping Liu; Norbert Peyerimhoff

    We study local properties of the Bakry–Émery curvature function ${\mathcal{K}}_{G,x}:(0,\infty ]\rightarrow \mathbb{R}$ at a vertex $x$ of a graph $G$ systematically. Here ${\mathcal{K}}_{G,x}({\mathcal{N}})$ is defined as the optimal curvature lower bound ${\mathcal{K}}$ in the Bakry–Émery curvature-dimension inequality $CD({\mathcal{K}},{\mathcal{N}})$ that $x$ satisfies. We provide upper and lower bounds for the curvature functions, introduce fundamental concepts like curvature sharpness and $S^{1}$ -out regularity, and relate the curvature functions of $G$ with various spectral properties of (weighted) graphs constructed from local structures of $G$ . We prove that the curvature functions of the Cartesian product of two graphs $G_{1},G_{2}$ are equal to an abstract product of curvature functions of $G_{1},G_{2}$ . We explore the curvature functions of Cayley graphs and many particular (families of) examples. We present various conjectures and construct an infinite increasing family of 6-regular graphs which satisfy $CD(0,\infty )$ but are not Cayley graphs.

    更新日期:2020-01-04
  • On Intrinsic Quadrics
    Can. J. Math. (IF 0.830) Pub Date : 2019-01-09
    Anne Fahrner; Jürgen Hausen

    An intrinsic quadric is a normal projective variety with a Cox ring defined by a single quadratic relation. We provide explicit descriptions of these varieties in the smooth case for small Picard numbers. As applications, we figure out in this setting the Fano examples and (affirmatively) test Fujita’s freeness conjecture.

    更新日期:2020-01-04
  • Eisenstein Series Arising from Jordan Algebras
    Can. J. Math. (IF 0.830) Pub Date : 2019-01-09
    Marcela Hanzer; Gordan Savin

    We describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.

    更新日期:2020-01-04
  • Growth of Homology of Centre-by-metabelian Pro- $p$ Groups
    Can. J. Math. (IF 0.830) Pub Date : 2019-01-09
    Dessislava H. Kochloukova; Aline G. S. Pinto

    For a centre-by-metabelian pro- $p$ group $G$ of type $\text{FP}_{2m}$ , for some $m\geqslant 1$ , we show that $\sup _{M\in {\mathcal{A}}}$ rk $H_{i}(M,\mathbb{Z}_{p})<\infty$ , for all $0\leqslant i\leqslant m$ , where ${\mathcal{A}}$ is the set of all subgroups of $p$ -power index in $G$ and, for a finitely generated abelian pro- $p$ group $V$ , rk $V=\dim V\otimes _{\mathbb{Z}_{p}}\mathbb{Q}_{p}$ .

    更新日期:2020-01-04
  • On Special Fiber Rings of Modules
    Can. J. Math. (IF 0.830) Pub Date : 2019-01-09
    Cleto B. Miranda-Neto

    We prove results concerning the multiplicity as well as the Cohen–Macaulay and Gorenstein properties of the special fiber ring $\mathscr{F}(E)$ of a finitely generated $R$ -module $E\subsetneq R^{e}$ over a Noetherian local ring $R$ with infinite residue field. Assuming that $R$ is Cohen–Macaulay of dimension 1 and that $E$ has finite colength in $R^{e}$ , our main result establishes an asymptotic length formula for the multiplicity of $\mathscr{F}(E)$ , which, in addition to being of independent interest, allows us to derive a Cohen–Macaulayness criterion and to detect a curious relation to the Buchsbaum–Rim multiplicity of $E$ in this setting. Further, we provide a Gorensteinness characterization for $\mathscr{F}(E)$ in the more general situation where $R$ is Cohen–Macaulay of arbitrary dimension and $E$ is not necessarily of finite colength, and we notice a constraint in terms of the second analytic deviation of the module $E$ if its reduction number is at least three.

    更新日期:2020-01-04
  • Comparison Geometry of Manifolds with Boundary under a Lower Weighted Ricci Curvature Bound
    Can. J. Math. (IF 0.830) Pub Date : 2018-10-24
    Yohei Sakurai

    We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric results.

    更新日期:2020-01-04
  • CJM volume 72 Issue 1 Cover and Front matter
    Can. J. Math. (IF 0.830) Pub Date : 2020-01-02

    None

    更新日期:2020-01-04
  • CJM volume 72 Issue 1 Cover and Back matter
    Can. J. Math. (IF 0.830) Pub Date : 2020-01-02

    None

    更新日期:2020-01-04
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