  We show that spatial patterns ("hotspots") may form in the crime model
  \begin{equation}
  \left\{\;
  \begin{aligned}
  u_{t} &= \tfrac{1}{\varepsilon}\Delta u - \tfrac{\chi}{\varepsilon} \nabla
\cdot \left(\tfrac{u}{v} \nabla v \right) - \varepsilon uv, \\
  v_{t} &= \Delta v - v + u v,
  \end{aligned}
  \right.
  \end{equation}
  which we consider in $\Omega = B_R(0) \subset \mathbb R^n$, $R > 0$, $n \geq
3$ with $\varepsilon > 0$, $\chi > 0$ and initial data $u_0$, $v_0$ with
sufficiently large initial mass $m := \int_\Omega u_0$.
  More precisely, for each $T > 0$ and fixed $\Omega$, $\chi$ and (large) $m$,
we construct initial data $v_0$ exhibiting the following unboundedness
phenomenon: Given any $M>0$, we can find $\varepsilon > 0$ such that the first
component of the associated maximal solution becomes larger than $M$ at some
point in $\Omega$ before the time $T$. Since the $L^1$ norm of $u$ is
decreasing, this implies that some heterogeneous structure must form.
  We do this by first constructing classical solutions to the nonlocal scalar
problem
  \[
  w_t = \Delta w + m \frac{w^{\chi+1}}{\int_\Omega w^\chi}
  \]
  from the solutions to the crime model by taking the limit $\varepsilon
\searrow 0$ under the assumption that the unboundedness phenomenon explicitly
does not occur on some interval $(0,T)$. We then construct initial data for
this scalar problem leading to blow-up before time $T$. As solutions to the
scalar problem are unique, this proves our central result by contradiction.
