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Enhanced specialization and microlocalization

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Abstract

Enhanced ind-sheaves provide a suitable framework for the irregular Riemann–Hilbert correspondence. In this paper, we show how Sato’s specialization and microlocalization functors have a natural enhancement, and discuss some of their properties.

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Notes

  1. We abusively call sheaf an object of the bounded derived category \(\mathrm {D}^{\mathrm {b}}(\mathbf {k}_M)\) of sheaves of \(\mathbf {k}\)-vector spaces on M, for a fixed base field \(\mathbf {k}\).

  2. Here we choose a different compactification from the one in [2, §B.2].

References

  1. D’Agnolo, A.: On the Laplace transform for tempered holomorphic functions. Int. Math. Res. Not. 2014(16), 4587–4623 (2014)

    Article  MathSciNet  Google Scholar 

  2. D’Agnolo, A., Hien, M., Morando, G., Sabbah, C.: Topological computations of some Stokes phenomena. Ann. Inst. Fourier 70(2), 739–808 (2020)

    Article  MathSciNet  Google Scholar 

  3. D’Agnolo, A., Kashiwara, M.: Riemann-Hilbert correspondence for holonomic D-modules. Publ. Math. Inst. Hautes Études Sci. 123(1), 69–197 (2016)

    Article  MathSciNet  Google Scholar 

  4. D’Agnolo, A., Kashiwara, M.: Enhanced perversities. J. Reine Angew. Math. (Crelle’s Journal) 751, 185–241 (2019)

    Article  MathSciNet  Google Scholar 

  5. Guillermou, S., Schapira, P.: Microlocal theory of sheaves and Tamarkin’s non displaceability theorem. In: Homological Mirror Symmetry and Tropical Geometry, Lecture Notes of the Unione Matematica Italiana 15, Springer, Berlin, 43–85 (2014)

  6. Kashiwara, M.: Riemann-Hilbert correspondence for irregular holonomic \({\cal{D}}\)-modules. Jpn. J. Math. 11(1), 113–149 (2016)

    Article  MathSciNet  Google Scholar 

  7. Kashiwara, M., Schapira, P.: Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften 292, Springer, Berlin, x+512 pp (1990)

  8. Kashiwara, M., Schapira, P.: Ind-sheaves, Astérisque 271, 136 pp (2001)

  9. Kashiwara, M., Schapira, P.: Irregular holonomic kernels and Laplace transform. Selecta Math. 22(1), 55–109 (2016)

    Article  MathSciNet  Google Scholar 

  10. Kashiwara, M., Schapira, P.: Regular and irregular holonomic D-modules, London Mathematical Society Lecture Note Series 433, Cambridge University Press, Cambridge, vi+111 pp (2016)

  11. Kashiwara, M., Schapira, P., Ivorra, F., Waschkies, I.: Microlocalization of ind-sheaves. In: Studies in Lie theory, 171–221, Progr. Math. 243, Birkhäuser (2006)

  12. Tamarkin, D.: Microlocal condition for non-displaceability. In: Algebraic and Analytic Microlocal Analysis, Springer Proc. in Math. & Stat. 269, 99–223 (2018)

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121, Padova, Italy

    Andrea D’Agnolo

  2. Kyoto University Institute for Advanced study, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Masaki Kashiwara

  3. Korea Institute for Advanced Study, Seoul, 02455, Korea

    Masaki Kashiwara

Authors
  1. Andrea D’Agnolo
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  2. Masaki Kashiwara
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Correspondence to Andrea D’Agnolo.

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The research of A.D’A. was partially supported by GNAMPA/INdAM. He acknowledges the kind hospitality at RIMS of Kyoto University during the preparation of this paper.

The research of M.K. was supported by Grant-in-Aid for Scientific Research (B) 15H03608, Japan Society for the Promotion of Science.

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D’Agnolo, A., Kashiwara, M. Enhanced specialization and microlocalization. Sel. Math. New Ser. 27, 7 (2021). https://doi.org/10.1007/s00029-020-00613-2

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  • DOI: https://doi.org/10.1007/s00029-020-00613-2

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