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Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we show how Satos specialization and microlocalization functors have a natural enhancement, and discuss some of their properties.
Let X be a smooth, connected, closed subvariety of a complex vector space V. The asymptotic cone as(X) is naturally equipped with a nearby cycles sheaf P coming from the specialization of X to as(X). We show that if X is transverse to infinity in a s
We construct an upgrade of the motivic volume by keeping track of dimensions in the Grothendieck ring of varieties. This produces a uniform refinement of the motivic volume and its birational version introduced by Kontsevich and Tschinkel to prove th
Let $R$ be a commutative noetherian ring, and $mathcal{Z}$ a stable under specialization subset of $Spec(R)$. We introduce a notion of $mathcal{Z}$-cofiniteness and study its main properties. In the case $dim(mathcal{Z})leq 1$, or $dim(R)leq 2$, or $
Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we give some precisions on nearby and vanishing cycles for enhanced perverse objects in dimension one. As an application, we give a top
We discuss a model of an economic community consisting of $N$ interacting agents. The state of each agent at any time is characterized, in general, by a mixed strategy profile drawn from a space of $s$ pure strategies. The community evolves as agents