• Corpus ID: 221516170

Induction equivalence for equivariant D-modules on rigid analytic spaces

@article{Ardakov2020InductionEF,
  title={Induction equivalence for equivariant D-modules on rigid analytic spaces},
  author={Konstantin Ardakov},
  journal={arXiv: Representation Theory},
  year={2020}
}
  • K. Ardakov
  • Published 7 September 2020
  • Mathematics
  • arXiv: Representation Theory
We prove an Induction Equivalence and a Kashiwara Equivalence for coadmissible equivariant D-modules on rigid analytic spaces. This allows us to completely classify such objects with support in a single orbit of a classical point with co-compact stabiliser. As an application, we use the locally analytic Beilinson-Bernstein equivalence to construct new examples of large families of topologically irreducible locally analytic representations of certain compact semisimple p-adic Lie groups. 
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References

SHOWING 1-10 OF 30 REFERENCES
D-modules on rigid analytic spaces II: Kashiwara's equivalence
We prove that the category of coadmissible D-cap-modules on a smooth rigid analytic space supported on a closed smooth subvariety is naturally equivalent to the category of coadmissible D-cap-modules
⌢𝒟-modules on rigid analytic spaces I
  • K. ArdakovS. Wadsley
  • Mathematics
    Journal für die reine und angewandte Mathematik (Crelles Journal)
  • 2019
We introduce a sheaf of infinite order differential operators {\overset{\frown}{\mathcal{D}}} on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent
Rigid analytic geometry and its applications
Preface.- Valued fields and normed spaces.- The projective line.- Affinoid algebras.- Rigid spaces.- Curves and their reductions.- Abelian varieties.- Points of rigid spaces, rigid cohomology.- Etale
Bounded linear endomorphisms of rigid analytic functions
Let K be a field of characteristic zero complete with respect to a non‐trivial, non‐Archimedean valuation. We relate the sheaf D︵ of infinite order differential operators on smooth rigid K ‐analytic
Algebras of p-adic distributions and admissible representations
Let G be a compact, locally L-analytic group, where L is a finite extension of Qp. Let K be a discretely valued extension field of L. We study the algebra D(G,K) of K-valued locally analytic
Banach space representations and Iwasawa theory
We develop a duality theory between the continuous representations of a compactp-adic Lie groupG in Banach spaces over a givenp-adic fieldK and certain compact modules over the completed group
Representations of Algebraic Groups
Our purpose here is to study the irreducible representations of semisimple algebraic groups of characteristic p 0, in particular the rational representations, and to determine all of the
Duality for Lie-Rinehart algebras and the modular class
We introduce a notion of duality for a Lie-Rinehart algebra giving certain bilinear pairings in its cohomology generalizing the usual notions of Poincar\'e duality in Lie algebra cohomology and de
Introduction to commutative algebra
* Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings *
Introduction to Affine Group Schemes
I The Basic Subject Matter.- 1 Affine Group Schemes.- 1.1 What We Are Talking About.- 1.2 Representable Functors.- 1.3 Natural Maps and Yoneda's Lemma.- 1.4 Hopf Algebras.- 1.5 Translating from
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