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We introduce a tensor compatibility condition for t-structures. For anyNoetherian scheme $X$, we prove that there is a one-to-one correspondencebetween the set of filtrations of Thomason subsets and the set of aisles ofcompactly generated tensor compatible t-structures on the derived category of$X$. This generalizes the earlier classification of compactly generatedt-structures for commutative rings to schemes. Hrbek and Nakamura havereformulated the famous telescope conjecture for t-structures. As anapplication of our main theorem, we prove that a tensor version of theconjecture is true for separated Noetherian schemes.

Compactly generated tensor t-structures on the derived category of a Noetherian scheme