Moreschini, Roberto (2018) Contramodules and applications to very flatness in commutative rings. [Magistrali biennali]
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Contramodules were first introduced by Eilenberg and Moore in 1965 alongside comodules over coalgebras or corings, but they achieved so little success that they were forgotten for three decades. Starting from the first years of the 21st century, contramodules appeared again in literature thanks mainly to Leonid Positselski's work. His attention and motivation towards the study of contramodules are driven by many potential applications in algebraic geometry, as it is easy intelligible from almost all of his papers. This work's main aim is to present some of the most elementary aspects about the topic as well as an application to very flatness over commutative rings, as in . This can be used as an introduction to the huge and more complicated theory developed by Positselski in further papers such as , ,  and . Many results are collected from Positselski's wide collection of studies, accurately detailed and integrated with other more classical topics which come into play alongside.
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