Journal
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
Volume 34, Issue 3, Pages 403-440Publisher
SOC MATHEMATIQUE FRANCE
DOI: 10.1016/S0012-9593(01)01064-3
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We construct a derived version of Grothendieck's Quot scheme which is a dg-scheme, i.e., an object RQuot of a certain nonabelian right derived category of schemes. It has the property of being manifestly smooth in an appropriate sense (whereas the usual Quot scheme is often singular). The usual scheme Quot is obtained from RQuot by degree 0 truncation. The construction of RQuot can be seen as realization of a part of the Derived Deformation Theory program, which proposes to replace all the moduli spaces arising in geometry 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.
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