<p>We prove that any scheme of finite type that is derived equivalent to an open subscheme of an abelian variety is itself an open subscheme of an abelian variety. In particular, every proper Fourier–Mukai partner of an abelian variety is again an abelian variety. Our argument differs from that of Huybrechts and Nieper-Wißkirchen for projective Fourier–Mukai partners: instead of their approach, we employ the Matsui spectrum. We further investigate the structure of the Matsui spectrum outside the Fourier–Mukai locus. For certain proper schemes, we show that the set of points lying outside the Fourier–Mukai locus in the Matsui spectrum has cardinality at least that of the base field. This indicates the presence of additional geometric structures beyond the derived-equivalent part, such as moduli spaces.</p>