• DOI:10.1112/S0010437X20007678
• Corpus ID: 52556558

Irregular perverse sheaves

@article{Kuwagaki2018IrregularPS,
  title={Irregular perverse sheaves},
  author={Tatsuki Kuwagaki},
  journal={Compositio Mathematica},
  year={2018},
  volume={157},
  pages={573 - 624}
}

• T. Kuwagaki
• Published 8 August 2018
• Mathematics
• Compositio Mathematica

We introduce irregular constructible sheaves, which are ${\mathbb {C}}$-constructible with coefficients in a finite version of the Novikov ring $\Lambda$ and special gradings. We show that the bounded derived category of cohomologically irregular constructible complexes is equivalent to the bounded derived category of holonomic ${\mathcal {D}}$-modules by a modification of D’Agnolo and Kashiwara's irregular Riemann–Hilbert correspondence. The bounded derived category of cohomologically irregular constructible complexes is equipped with the irregular perverse $t$-structure, which is a straightforward generalization of usual perverse $t$-structure, and we prove that its heart is equivalent to the abelian category of holonomic ${\mathcal {D}}$-modules. We also develop the algebraic version of the theory.