Relative perfect complexes
Relative perfect complexes
Abstract Let $$f :X \rightarrow Y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo>→</mml:mo> <mml:mi>Y</mml:mi> </mml:mrow> </mml:math> be a morphism of concentrated schemes. We characterize f -perfect complexes $${\mathscr {E}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> as those such that the functor $${\mathscr {E}}\otimes ^{\varvec{\textsf{L}}}_X \varvec{\textsf{L}}f^*-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:msubsup> <mml:mo>⊗</mml:mo> <mml:mi>X</mml:mi> …