The formalisation of informal security-providers has important consequences for citizenship, the rule of law, and human rights. We examine these policies in Burkina Faso, where formalisation has led to concerns about vigilante justice and ethnic targeting. Although African governments' reliance on informal security provision is well-documented, less is known about the origins of formalisation policies. To advance theory-building in this domain, this paper examines the political logic of empowering self-defence groups through the study of Burkina Faso's 2022 junta government, with comparisons to two prior regimes. We argue that formalisation is not only a mechanism for overcoming vexing security challenges, but is a tool used by leaders to build legitimacy and strengthen the regime's grip on power. In doing so, the article contributes insights into the origins of governmental policies towards self-defence groups, with implications for the study of political legitimacy, security provision and citizen–state relations.

We describe the Galois action on the middle $\ell $ -adic cohomology of smooth, projective fourfolds $K_A(v)$ that occur as a fiber of the Albanese morphism on moduli spaces of sheaves on an abelian surface A with Mukai vector v. We show this action is determined by the action on $H^2_{\mathrm {\acute{e}t}}(A_{\bar {k}},{\mathbb Q}_{\ell }(1))$ and on a subgroup $G_A(v) \leqslant (A\times \hat {A})[3]$ , which depends on v. This generalizes the analysis carried out by Hassett and Tschinkel over ${\mathbb C}$ [21]. As a consequence, over number fields, we give a condition under which $K_2(A)$ and $K_2(\hat {A})$ are not derived equivalent.

The points of $G_A(v)$ correspond to involutions of $K_A(v)$ . Over ${\mathbb C}$ , they are known to be symplectic and contained in the kernel of the map $\operatorname {\mathrm {Aut}}(K_A(v))\to \mathrm {O}(H^2(K_A(v),{\mathbb Z}))$ . We describe this kernel for all varieties $K_A(v)$ of dimension at least $4$ .

When $K_A(v)$ is a fourfold over a field of characteristic 0, the fixed-point loci of the involutions contain K3 surfaces whose cycle classes span a large portion of the middle cohomology. We examine the fixed-point locus on fourfolds $K_A(0,l,s)$ over ${\mathbb C}$ where A is $(1,3)$ -polarized, finding the K3 surface to be elliptically fibered under a Lagrangian fibration of $K_A(0,l,s)$ .