2,259 research outputs found
Relative Riemann-Hilbert correspondence in dimension one
We prove that, on a Riemann surface, the functor constructed
in a previous work as a right quasi-inverse of the solution functor from the
bounded derived category of regular relative holonomic modules to that of
relative constructible complexes satisfies the left quasi-inverse property in a
generic sense.Comment: 10 pages. V2: revised version, some mistake corrected, improvement of
the presentation. V3: final version to be publishe
-Structures for Relative -Modules and -Exactness of the de Rham Functor
This paper is a contribution to the study of relative holonomic
-modules. Contrary to the absolute case, the standard
-structure on holonomic -modules is not preserved by duality
and hence the solution functor is no longer -exact with respect to the
canonical, resp. middle-perverse, -structures. We provide an explicit
description of these dual -structures. When the parameter space is
1-dimensional, we use this description to prove that the solution functor as
well as the relative Riemann-Hilbert functor are -exact with respect to the
dual -structure and to the middle-perverse one while the de Rham functor is
-exact for the canonical, resp. middle-perverse, -structures and their
duals.Comment: Final version to appear in Journal of Algebr
Presentations for monoids of finite partial isometries
In this paper we give presentations for the monoid of all
partial isometries on and for its submonoid
of all order-preserving partial isometries.Comment: 11 pages, submitte
t-structures for relative D-modules and t-exactness of the de Rham functor
This paper is a contribution to the study of relative holonomic D-modules. Contrary to the absolute case, the standard t-structure on holonomic D-modules is not preserved by duality and hence the solution functor is no longer t-exact with respect to the canonical, resp. middle-perverse, t-structure.
We provide an explicit description of these dual t-structures. We use this description to prove that the solution functor as well as the relative Riemann-Hilbert functor are t-exact with respect to the dual t-structure and to the middle-perverse one while the de Rham functor is t-exact for the canonical, resp. middle-perverse, t-structure and their duals
Involutivity of truncated microsupports
Using a result of J-M. Bony, we prove the weak involutivity of truncated
microsupports. More precisely, given a sheaf on a real manifold and an
integer , if two functions vanish on the truncated microsupport ,
then so does their Poisson bracket.Comment: 9 page
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