Abstract:  Contramodules are module-like algebraic structures endowed with infinite summation or, occasionally, integration operations, understood algebraically as infinitary linear operations subject to natural axioms.  Simple counterexamples show that the contramodule infinite sum cannot be interpreted as any kind of limit of finite partial sums.  Geometrically, contramodules appear as a kind of module structures over formal schemes and ind-schemes, which are an algebro-geometric version of the differential-geometric concept of a tubular neighborhood.  Introduced originally by Eilenberg and Moore in 1965, contramodules experience a small renaissance now after being all but forgotten for three decades between 1970-2000.

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at Schreiber building 006