arXiv:1001.2355 Semi-topological algebraic geometry and Riemann-Roch theorem from arXiv Front: math.KT by J. H. Teh We consider algebraic varieties parametrized continuously by topological spaces. The schemes formed are non-Noetherian but they appear naturally in many places. We define Lawson homology, morphic cohomology, construct Chern classes and develop some intersection theory for semi-topological schemes. A Grothendieck-Riemann-Roch type theorem in morphic cohomology for some closed imbeddings is proved. Some new invariants like semi-topological cobordism groups, semi-topological Chow groups and higher derived categories of coherent sheaves are defined.
nLab page on Semitopological algebraic geometry