RIEMANN-HILBERT CORRESPONDENCE for MIXED TWISTOR D-MODULES

Teresa Monteiro Fernandes; Claude Sabbah

doi:10.1017/S1474748017000184

RIEMANN-HILBERT CORRESPONDENCE for MIXED TWISTOR D-MODULES

Teresa Monteiro Fernandes, Claude Sabbah

Faculdade de Ciências, Universidade de Lisboa

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce the notion of regularity for a relative holonomic -module in the sense of Monteiro Fernandes and Sabbah [Internat. Math. Res. Not. (21) (2013), 4961-4984]. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of relative constructible complexes is essentially surjective by constructing a right quasi-inverse functor. When restricted to relative -modules underlying a regular mixed twistor -module, this functor satisfies the left quasi-inverse property.

Original language	English
Pages (from-to)	629-672
Number of pages	44
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	18
Issue number	3
DOIs	https://doi.org/10.1017/S1474748017000184
Publication status	Published - 1 May 2019

Keywords

holonomic relative D-module
mixed twistor D-module
regularity
relative constructible sheaf
relative perverse sheaf

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10.1017/S1474748017000184

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title = "RIEMANN-HILBERT CORRESPONDENCE for MIXED TWISTOR D-MODULES",

abstract = "We introduce the notion of regularity for a relative holonomic -module in the sense of Monteiro Fernandes and Sabbah [Internat. Math. Res. Not. (21) (2013), 4961-4984]. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of relative constructible complexes is essentially surjective by constructing a right quasi-inverse functor. When restricted to relative -modules underlying a regular mixed twistor -module, this functor satisfies the left quasi-inverse property.",

keywords = "holonomic relative D-module, mixed twistor D-module, regularity, relative constructible sheaf, relative perverse sheaf",

author = "\{Monteiro Fernandes\}, Teresa and Claude Sabbah",

note = "Publisher Copyright: {\textcopyright} Cambridge University Press 2017.",

year = "2019",

month = may,

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doi = "10.1017/S1474748017000184",

language = "English",

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AU - Monteiro Fernandes, Teresa

AU - Sabbah, Claude

N1 - Publisher Copyright: © Cambridge University Press 2017.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - We introduce the notion of regularity for a relative holonomic -module in the sense of Monteiro Fernandes and Sabbah [Internat. Math. Res. Not. (21) (2013), 4961-4984]. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of relative constructible complexes is essentially surjective by constructing a right quasi-inverse functor. When restricted to relative -modules underlying a regular mixed twistor -module, this functor satisfies the left quasi-inverse property.

AB - We introduce the notion of regularity for a relative holonomic -module in the sense of Monteiro Fernandes and Sabbah [Internat. Math. Res. Not. (21) (2013), 4961-4984]. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of relative constructible complexes is essentially surjective by constructing a right quasi-inverse functor. When restricted to relative -modules underlying a regular mixed twistor -module, this functor satisfies the left quasi-inverse property.

KW - holonomic relative D-module

KW - mixed twistor D-module

KW - regularity

KW - relative constructible sheaf

KW - relative perverse sheaf

U2 - 10.1017/S1474748017000184

DO - 10.1017/S1474748017000184

M3 - Article

AN - SCOPUS:85019884911

SN - 1474-7480

VL - 18

SP - 629

EP - 672

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 3

ER -

RIEMANN-HILBERT CORRESPONDENCE for MIXED TWISTOR D-MODULES

Abstract

Keywords

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