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It is shown that the construct of supertopological spaces and continuous maps is topological.
2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new and transparent proof that...
Let be a semidualizing module over a commutative ring. We first investigate the properties of -dual, -torsionless and -reflexive modules. Then we characterize some rings such as coherent rings, -coherent rings and FP-injectivity of using -dual, -torsionless and -reflexive properties of some special modules.
Let X be a separated scheme of finite type on a field k, the characteristic of k being assumed not equal to 2. We construct a duality for complexes of sheaves of Ox modules with maps differential operators of order ≤ 1. This theory is an extension of the theory built by R. Hartshorne for complexes with linear maps.
Un survol des conjectures de Drinfeld, Beilinson, Gaitsgory et al. et de résultats de Gaitsgory sur la correspondance de Langlands quantique.
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