  Balmer defined the tensor triangulated spectrum $\operatorname{Spec}_\otimes
\mathcal{T}$ of a tensor triangulated category $(\mathcal{T},\otimes)$ and
showed that for a variety $X$, we have the reconstruction $X \cong
\operatorname{Spec}_{\otimes_{\mathscr{O}_X}^{\mathbb{L}}}\operatorname{Perf}
X$. In the absence of the tensor structure, Matsui recently introduced the
triangular spectrum $\operatorname{Spec}_\vartriangle \mathcal{T}$ of a
triangulated category $\mathcal{T}$ and showed that there exists an immersion
$X \cong
\operatorname{Spec}_{\otimes_{\mathscr{O}_X}^{\mathbb{L}}}\operatorname{Perf} X
\subset \operatorname{Spec}_\vartriangle \operatorname{Perf} X$. In this paper,
we construct a scheme $\operatorname{Spec}^{\mathsf{FM}} \mathcal{T} \subset
\operatorname{Spec}_\vartriangle \mathcal{T}$, called the Fourier-Mukai (FM)
locus, by gathering all varieties $X$ satisfying $\operatorname{Perf} X \simeq
\mathcal{T}$. Those varieties are called FM partners of $\mathcal{T}$ and
immersed into $\operatorname{Spec}_\vartriangle \mathcal{T}$ as tensor
triangulated spectra. We present a variety of examples illustrating how
geometric and birational properties of FM partners are reflected in the way
their tensor triangulated spectra are glued in the FM locus. Finally, we
compare the FM locus with other loci within the triangular spectrum admitting
categorical characterizations, and in particular, make a precise conjecture
about the relation of the FM locus with the Serre invariant locus.
