
TL;DR
This paper explores the structure of Artin perverse sheaves, establishing t-structures on Artin $ ext{l}$-adic complexes for schemes of dimension less than 2, and analyzing their properties over finite fields.
Contribution
It introduces a t-structure on Artin $ ext{l}$-adic complexes for low-dimensional schemes and describes the heart explicitly in the 1-dimensional case, also constructing a perverse homotopy t-structure over finite fields.
Findings
The perverse t-structure induces a t-structure on Artin $ ext{l}$-adic complexes for schemes of dimension less than 2.
The heart of this t-structure can be explicitly described in the 1-dimensional case.
The perverse homotopy t-structure over finite fields is the best approximation of the perverse t-structure.
Abstract
We show that the perverse t-structure induces a t-structure on the category of Artin -adic complexes when is an excellent scheme of dimension less than and provide a counter-example in dimension . The heart of this t-structure can be described explicitly in terms of representations in the case of -dimensional schemes. When is of finite type over a finite field, we also construct a perverse homotopy t-structure over and show that it is the best possible approximation of the perverse t-structure. We describe the simple objects of its heart and show that the weightless truncation functor is t-exact. We also show that the weightless intersection complex is a simple Artin homotopy perverse…
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