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Artículo
Algebraic computation of some intersection D-modules
(Springer, 2006)
Let X be a complex analytic manifold, D ⊂ X a locally quasi-homogeneous free divisor, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on X − D. In this ...
Artículo
Coefficient fields and scalar extension in positive characteristic
(Elsevier, 2005-03-15)
Let k be a perfect field of positive characteristic, k(t)per the perfect closure of k(t) and A = k[[X1, . . . , Xn]]. We show that for any maximal ideal n of A′ = k(t)per ⊗k A, the elements in Ac′ n which are annihilated ...
Artículo
Continuous division of linear differential operators and faithful flatness of D∞X over DX
(Société Mathématique de France, 2004)
In these notes we prove the faithful flatness of the sheaf of infinite order linear differential operators over the sheaf of finite order linear differential operators on a complex analytic manifold. We give the ...
Artículo
A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors
(Elsevier, 2015-08-20)
In this paper we prove that the Bernstein-Sato polynomial of any free divisor for which the D[s]-module D[s]h s admits a Spencer logarithmic resolution satisfies the symmetry property b(−s−2) = ±b(s). This applies in ...
Artículo
On the logarithmic comparison theorem for integrable logarithmic connections
(London Mathematical Society, 2009)
Let X be a complex analytic manifold, D ⊂ X a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), j : U = X − D ֒→ X the corresponding open inclusion, E an integrable logarithmic ...
Artículo
Hasse-Schmidt derivations, divided powers and differential smoothness
(Association des Annales de l'Institut Fourier, 2009)
Let k be a commutative ring, A a commutative k-algebra and D the filtered ring of k-linear differential operators of A. We prove that: (1) The graded ring gr D admits a canonical embedding θ into the graded dual of the ...
Artículo
On the modules of m-integrable derivations in non-zero characteristic
(Elsevier, 2012-03-20)
Let k be a commutative ring and A a commutative k-algebra. Given a positive integer m, or m = ∞, we say that a k-linear derivation δ of A is m-integrable if it extends up to a Hasse–Schmidt derivation D = (Id, D1 = δ, ...
Artículo
Dualité et comparaison sur les complexes de de Rham logarithmiques par rapport aux diviseurs libres
(Association des Annales de l'Institut Fourier, 2005)
Let X be a complex analytic manifold and D \subset X a free divisor. Integrable logarithmic connections along D can be seen as locally free {\cal O}_X-modules endowed with a (left) module structure over the ring of logarithmic ...
Artículo
The local duality theorem in D-module theory
(Société Mathématique de France, 2004)
These notes are devoted to the Local Duality Theorem for D-modules, which asserts that the topological Grothendieck-Verdier duality exchanges the de Rham complex and the solution complex of holonomic modules over a complex ...
Artículo
Le théorème du symbole total d’un opérateur différentiel p-adique
(Consejo Superior de Investigaciones Científicas, 2010)
Let X † be a smooth †-scheme (in the sense of Meredith) over a complete discrete valuation ring (V,m) of unequal characteristics (0, p) and let D†X†/V be the sheaf of V -linear endomorphisms of OX† whose reduction modulo ...