Derived quot schemes

We construct a "derived" version of Grothendieck's Quot scheme which is a d g-scheme, i.e., an object RQuot of a certain nonabelian right derived categ ory of schemes. It has the property of being manifestly smooth in an approp riate sense (whereas the usual Quot scheme is often singular). The usual sc heme Quot is obtained from RQuot by degree 0 truncation. The construction o f RQuot can be seen as realization of a part of the Derived Deformation The ory program, which proposes to replace all the moduli spaces arising in geo metry by their derived versions by retaining the information about all the higher cohomology instead of H-1 in the classical theory. (C) 2001 Editions scientifiques et medicales Elsevier SAS.