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### Generalized Behrend version for Grothendieck-Lefschetz trace formula

[MOVED HERE FROM MSE.] The statement of the Grothendieck-Lefschetz fixed point theorem is well-known. For a proper algebraic variety $X$ over $\mathbb F_q$, \#X(\mathbb F_q) =\sum_i (−1)^i Tr(Fr_X, ...
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### Definition for equivariant $l$-adic sheaves

What is the definition of equivariant $l$-adic or ($\mathbb{Z}_l$-) sheaves? Suppose $G$ acts on $X$, I could pick a $G$-equivariant etale sheaf of $\mathbb{Z}/l^n$ module on $X$ for each $n$, and ...
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### IC sheaves and formal neighbourhoods

Let $X$ and $Y$ be two schemes of finite type over a finite field $\mathbb F_q$. Let $x$ (resp. $y$) be an $\mathbb F_q$-point of $X$ (resp. of $Y$). Let now $l$ be a prime which is prime to $q$. ...
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### Convolution of $\ell$-adic sheaves and group homomorphisms

This question follows this one , where I defined convolution of $\ell$-adic/perverse sheaves. Here I am working with a perfect field $k$ ($char(k)\neq l$) and with a smooth separated groupscheme $G$ ...
### Convolution of $\ell$-adic sheaves is commutative if the group is commutative
[This is a duplicate of this question on Stackexchange] I am trying to figure out how to prove a very basic statement about convolution of $\ell$-adic/perverse sheaves in Katz's "Rigid local systems" ...
For constructible sheaves $\mathcal F$ on real analytic manifolds $X$, there is a notion of the singular support $SS(\mathcal F)$ which is a radially invariant singular Lagrangian subset of the ...