Abstract
In this paper we study Frobenius bimodules between noncommutative spaces (quasi-schemes), developing some of their basic properties. If X and Y are spaces, we study those Frobenius X, Y-bimodules X M Y satisfying properties that are natural in the context of noncommutative algebraic geometry, focusing in particular on cartain “local” conditions on M . As applications, we prove decomposition and gluing theorems for those Frobenius bimodules which have good local properties. Additionally, when X and Y are schemes we relate Frobenius X, Y-bimodules to the sheaf X, Y-bimodules introduced by van den Bergh in (J. Algebra 184 (1996) 435–490).
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