Irregular perverse sheaves

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