Microlocal categories over Novikov rings

In this paper, we define a family of categories for each Weinstein manifold, which is an enhanced version of the category first introduced by Tamarkin.

Using our categories, for any (possibly non-exact immersed) Lagrangian brane, we develop a theory of sheaf quantization generalizing the previous researches.

In particular, our theory involves the notion of a sheaf-theoretic bounding cochain, which is a conjectural counterpart of the theory of Fukaya--Oh--Ohta--Ono.

We also study several structures of our categories for sufficiently Weinstein manifolds and properties known in the classical Tamarkin category; intersection points estimates, interleaving distances, energy stability with respect to Guillermou--Kashiwara--Schapira autoequivalence, and the completeness of the distance.

We conjecture that our category is equivalent to a Fukaya category defined over the Novikov ring.