scholarly journals Inertial and Hodge–Tate weights of crystalline representations

2019 ◽  
Vol 376 (1-2) ◽  
pp. 645-681 ◽  
Author(s):  
Robin Bartlett
Keyword(s):  
Full Subcategory ◽  
Crystalline Representations ◽  
Crystalline Representation

AbstractLet K be an unramified extension of $${\mathbb {Q}}_p$$Qp and $$\rho :G_K \rightarrow {\text {GL}}_n(\overline{{\mathbb {Z}}}_p)$$ρ:GK→GLn(Z¯p) a crystalline representation. If the Hodge–Tate weights of $$\rho $$ρ differ by at most p then we show that these weights are contained in a natural collection of weights depending only on the restriction to inertia of $${\overline{\rho }} = \rho \otimes _{\overline{{\mathbb {Z}}}_p} \overline{{\mathbb {F}}}_p$$ρ¯=ρ⊗Z¯pF¯p. Our methods involve the study of a full subcategory of p-torsion Breuil–Kisin modules which we view as extending Fontaine–Laffaille theory to filtrations of length p.

scholarly journals Reflective subcategories

2000 ◽  
Vol 42 (1) ◽  
pp. 97-113 ◽  
Author(s):  
Juan Rada ◽  
Manuel Saorín ◽  
Alberto del Valle
Keyword(s):  
Category Theory ◽  
Full Subcategory ◽  
Subject Classification ◽  
Adjoint Functor ◽  
Direct Limits ◽  
The Relationship ◽  
Good Behaviour

Given a full subcategory [Fscr ] of a category [Ascr ], the existence of left [Fscr ]-approximations (or [Fscr ]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that [Fscr ] is reflective in [Ascr ], in the classical terminology of category theory.In the first part of the paper we establish, for a rather general [Ascr ], the relationship between reflectivity and covariant finiteness of [Fscr ] in [Ascr ], and generalize Freyd's adjoint functor theorem (for inclusion functors) to not necessarily complete categories. Also, we study the good behaviour of reflections with respect to direct limits. Most results in this part are dualizable, thus providing corresponding versions for coreflective subcategories.In the second half of the paper we give several examples of reflective subcategories of abelian and module categories, mainly of subcategories of the form Copres (M) and Add (M). The second case covers the study of all covariantly finite, generalized Krull-Schmidt subcategories of {\rm Mod}_{R}, and has some connections with the “pure-semisimple conjecture”.1991 Mathematics Subject Classification 18A40, 16D90, 16E70.

scholarly journals Reflective Full Subcategories of the Category ofL-Posets

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Hongping Liu ◽  
Qingguo Li ◽  
Xiangnan Zhou
Keyword(s):  
Special Class ◽  
Full Subcategory ◽  
Closure Operators ◽  
The Relationship ◽  
Equivalent Description

This paper focuses on the relationship betweenL-posets and completeL-lattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of completeL-lattices is a reflective full subcategory of the category ofL-posets with appropriate morphisms. Moreover, we characterize the Dedekind-MacNeille completions ofL-posets and provide an equivalent description for them.

Linear types and approximation

2000 ◽  
Vol 10 (6) ◽  
pp. 719-745 ◽  
Author(s):  
MICHAEL HUTH ◽  
ACHIM JUNG ◽  
KLAUS KEIMEL
Keyword(s):  
Full Subcategory ◽  
Linear Logic ◽  
Domain Theory ◽  
Classical Domain ◽  
Complete Distributivity ◽  
Linear Types ◽  
Continuous Lattices

We study continuous lattices with maps that preserve all suprema rather than only directed ones. We introduce the (full) subcategory of FS-lattices, which turns out to be *-autonomous, and in fact maximal with this property. FS-lattices are studied in the presence of distributivity and algebraicity. The theory is extremely rich with numerous connections to classical Domain Theory, complete distributivity, Topology and models of Linear Logic.

scholarly journals THE UNITY AND IDENTITY OF DECIDABLE OBJECTS AND DOUBLE-NEGATION SHEAVES

2018 ◽  
Vol 83 (04) ◽  
pp. 1667-1679
Author(s):  
MATÍAS MENNI
Keyword(s):  
Differential Geometry ◽  
Algebraic Geometry ◽  
Algebraic Topology ◽  
Full Subcategory ◽  
Sufficient Conditions ◽  
Double Negation ◽  
Synthetic Differential Geometry ◽  
Simplicial Sets ◽  
Image Position

AbstractLet ${\cal E}$ be a topos, ${\rm{Dec}}\left( {\cal E} \right) \to {\cal E}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg \,\,\neg }} \to {\cal E}$ be the full subcategory of double-negation sheaves. We give sufficient conditions for the existence of a Unity and Identity ${\cal E} \to {\cal S}$ for the two subcategories of ${\cal E}$ above, making them Adjointly Opposite. Typical examples of such ${\cal E}$ include many ‘gros’ toposes in Algebraic Geometry, simplicial sets and other toposes of ‘combinatorial’ spaces in Algebraic Topology, and certain models of Synthetic Differential Geometry.

Quasi-Splitting Exact Sequence

1971 ◽  
Vol 23 (3) ◽  
pp. 503-506
Author(s):  
Hsiang-Dah Hou
Keyword(s):  
Exact Sequence ◽  
Full Subcategory ◽  
Abelian Category ◽  
Image Position

Let R be a ring with 1 ≠ 0 and α, β, γ R-endomorphisms of R-modules A, B, and C respectively. We shall denote by M(R) the category of R-modules, and by End(R) the category of R-endomorphisms. For objects α and β of End(R) a morphism λ: α → β is an R-homomorphism such that λα = β λ. We shall denote by Idm(R) the full subcategory of End(R) whose objects are idempotents. Idm(R) is an abelian category, ker, coker and im are constructed in the naive way and henceis exact in M(R) if and only ifis exact in Idm(R), where the domains of α,β, and γ are A, B, and C respectively. One sees that End (R) as well as Idm(R) is abelian.

scholarly journals BGG CATEGORY FOR THE QUANTUM SCHRÖDINGER ALGEBRA

2020 ◽  
pp. 1-14
Author(s):  
GENQIANG LIU ◽  
YANG LI
Keyword(s):  
Complex Number ◽  
Full Subcategory ◽  
Weyl Algebra ◽  
Central Charge ◽  
Enveloping Algebra ◽  
Root Of Unity ◽  
Finite Dimensional ◽  
Quantum Weyl Algebra ◽  
Schrödinger Algebra

Abstract In 1996, a q-deformation of the universal enveloping algebra of the Schrödinger Lie algebra was introduced in Dobrev et al. [J. Phys. A 29 (1996) 5909–5918.]. This algebra is called the quantum Schrödinger algebra. In this paper, we study the Bernstein-Gelfand-Gelfand (BGG) category $\mathcal{O}$ for the quantum Schrödinger algebra $U_q(\mathfrak{s})$ , where q is a nonzero complex number which is not a root of unity. If the central charge $\dot z\neq 0$ , using the module $B_{\dot z}$ over the quantum Weyl algebra $H_q$ , we show that there is an equivalence between the full subcategory $\mathcal{O}[\dot Z]$ consisting of modules with the central charge $\dot z$ and the BGG category $\mathcal{O}^{(\mathfrak{sl}_2)}$ for the quantum group $U_q(\mathfrak{sl}_2)$ . In the case that $\dot z = 0$ , we study the subcategory $\mathcal{A}$ consisting of finite dimensional $U_q(\mathfrak{s})$ -modules of type 1 with zero action of Z. We directly construct an equivalence functor from $\mathcal{A}$ to the category of finite dimensional representations of an infinite quiver with some quadratic relations. As a corollary, we show that the category of finite dimensional $U_q(\mathfrak{s})$ -modules is wild.

scholarly journals Tripleableness of pro-c-groups

1976 ◽  
Vol 21 (3) ◽  
pp. 299-309 ◽  
Author(s):  
Lim Chong-Keang
Keyword(s):  
Algebraic Number ◽  
Full Subcategory ◽  
Forgetful Functor ◽  
Galois Groups ◽  
Inverse Limits ◽  
Discrete Groups ◽  
Profinite Groups ◽  
Finite Products

Let C be a nontrivial full subcategory of the category F of finite discrete groups and continuous homomorphisms, closed under subobjects, quotient and finite products. We consider the category PC of pro-C-groups and continuous homomorphisms (i.e. inverse limits of C-groups) which forms a variety in category PF of profinite groups and continuous homomorphisms. The study of pro-Cgroups is motivated by their occurrence as Galois groups of filed extensions in algebraic number thory (see Serre (1965)). The purpose of this paper is to study the tripleableness of the forgetful functors from PC to various underlying categories. It is also shown that PC is equivalent to the category of algebras of the theory of the forgetful functor from C to S (the category of sets and mappings).

scholarly journals Realizing the Braided Temperley–Lieb–Jones C*-Tensor Categories as Hilbert C*-Modules

2020 ◽  
Vol 380 (1) ◽  
pp. 103-130
Author(s):  
Andreas Næs Aaserud ◽  
David E. Evans
Keyword(s):  
Orthonormal Basis ◽  
Full Subcategory ◽  
Tensor Category ◽  
Compact Operators ◽  
Finitely Generated ◽  
Tensor Categories ◽  
C Algebra

Abstract We associate to each Temperley–Lieb–Jones C*-tensor category $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ T L J ( δ ) with parameter $$\delta $$ δ in the discrete range $$\{2\cos (\pi /(k+2)):\,k=1,2,\ldots \}\cup \{2\}$$ { 2 cos ( π / ( k + 2 ) ) : k = 1 , 2 , … } ∪ { 2 } a certain C*-algebra $${\mathcal {B}}$$ B of compact operators. We use the unitary braiding on $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ T L J ( δ ) to equip the category $$\mathrm {Mod}_{{\mathcal {B}}}$$ Mod B of (right) Hilbert $${\mathcal {B}}$$ B -modules with the structure of a braided C*-tensor category. We show that $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ T L J ( δ ) is equivalent, as a braided C*-tensor category, to the full subcategory $$\mathrm {Mod}_{{\mathcal {B}}}^f$$ Mod B f of $$\mathrm {Mod}_{{\mathcal {B}}}$$ Mod B whose objects are those modules which admit a finite orthonormal basis. Finally, we indicate how these considerations generalize to arbitrary finitely generated rigid braided C*-tensor categories.

scholarly journals An algorithm for computing the reduction of 2-dimensional crystalline representations of Gal(ℚ¯p/ℚp)

2018 ◽  
Vol 14 (07) ◽  
pp. 1857-1894 ◽  
Author(s):  
Sandra Rozensztajn
Keyword(s):  
Galois Representation ◽  
Langlands Correspondence ◽  
Dimension Formula ◽  
Crystalline Representations ◽  
Reduction Modulo

We describe an algorithm to compute the reduction modulo [Formula: see text] of a crystalline Galois representation of dimension [Formula: see text] of [Formula: see text] with distinct Hodge–Tate weights via the semi-simple modulo [Formula: see text] Langlands correspondence. We give some examples computed with an implementation of this algorithm in SAGE.

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