  We define and characterise small support for complexes over non-Noetherian
rings and in this context prove a vanishing theorem for modules. Our definition
of support makes sense for any rigidly compactly generated tensor triangulated
category. Working in this generality, we establish basic properties of support
and investigate when it detects vanishing. We use pointless topology to relate
support, the topology of the Balmer spectrum, and the structure of the
idempotent Bousfield lattice.
