Tempered solutions of 𝒟 -modules on complex curves and formal invariants

Giovanni Morando[1]

  • [1] Università di Padova Dipartimento di Matematica Pura ed Applicata Via Trieste 63 35121 Padova (Italy) and Universidade de Lisboa Centro de Álgebra Av. Prof. Gama Pinto, 2 1649-003 Lisboa (Portugal)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 4, page 1611-1639
  • ISSN: 0373-0956

Abstract

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Let X be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of 𝒟 -modules on X induces a fully faithful functor on a subcategory of germs of formal holonomic 𝒟 -modules. Further, given a germ ℳ of holonomic 𝒟 -module, we obtain some results linking the subanalytic sheaf of tempered solutions of ℳ and the classical formal and analytic invariants of ℳ .

How to cite

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Morando, Giovanni. "Tempered solutions of $\mathcal{D}$-modules on complex curves and formal invariants." Annales de l’institut Fourier 59.4 (2009): 1611-1639. <http://eudml.org/doc/10436>.

@article{Morando2009,
abstract = {Let $X$ be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of $\mathcal\{D\}$-modules on $X$ induces a fully faithful functor on a subcategory of germs of formal holonomic $\mathcal\{D\}$-modules. Further, given a germ $\mathcal\{M\}$ of holonomic $\mathcal\{D\}$-module, we obtain some results linking the subanalytic sheaf of tempered solutions of $\mathcal\{M\}$ and the classical formal and analytic invariants of $\mathcal\{M\}$.},
affiliation = {Università di Padova Dipartimento di Matematica Pura ed Applicata Via Trieste 63 35121 Padova (Italy) and Universidade de Lisboa Centro de Álgebra Av. Prof. Gama Pinto, 2 1649-003 Lisboa (Portugal)},
author = {Morando, Giovanni},
journal = {Annales de l’institut Fourier},
keywords = {$\mathcal\{D\}$-modules; irregular singularities; tempered holomorphic functions; subanalytic; -modules},
language = {eng},
number = {4},
pages = {1611-1639},
publisher = {Association des Annales de l’institut Fourier},
title = {Tempered solutions of $\mathcal\{D\}$-modules on complex curves and formal invariants},
url = {http://eudml.org/doc/10436},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Morando, Giovanni
TI - Tempered solutions of $\mathcal{D}$-modules on complex curves and formal invariants
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 4
SP - 1611
EP - 1639
AB - Let $X$ be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of $\mathcal{D}$-modules on $X$ induces a fully faithful functor on a subcategory of germs of formal holonomic $\mathcal{D}$-modules. Further, given a germ $\mathcal{M}$ of holonomic $\mathcal{D}$-module, we obtain some results linking the subanalytic sheaf of tempered solutions of $\mathcal{M}$ and the classical formal and analytic invariants of $\mathcal{M}$.
LA - eng
KW - $\mathcal{D}$-modules; irregular singularities; tempered holomorphic functions; subanalytic; -modules
UR - http://eudml.org/doc/10436
ER -

References

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