Matches in SemOpenAlex for { <https://semopenalex.org/work/W76883030> ?p ?o ?g. }
- W76883030 abstract "Let $A$ be a differential graded algebra with cohomology ring $H^*A$. A graded module over $H^*A$ is called emph{realisable} if it is (up to direct summands) of the form $H^*M$ for some differential graded $A$-module $M$. Benson, Krause and Schwede have stated a local and a global obstruction for realisability. The global obstruction is given by the Hochschild class determined by the secondary multiplication of the $A_{infty}$-algebra structure of $H^*A$. In this thesis we mainly consider differential graded algebras $A$ with graded-commutative cohomology ring. We show that a finitely presented graded $H^*A$-module $X$ is realisable if and only if its $mathfrak{p}$-localisation $X_{mathfrak{p}}$ is realisable for all graded prime ideals $mathfrak{p}$ of $H^*A$. In order to obtain such a local-global principle also for the global obstruction, we define the emph{localisation of a differential graded algebra $A$ at a graded prime $mathfrak{p}$ of $H^*A$}, denoted by $A_{mathfrak{p}}$, and show the existence of a morphism of differential graded algebras inducing the canonical map $H^*A to (H^*A)_{mathfrak{p}}$ in cohomology. The latter result actually holds in a much more general setting: we prove that every smashing localisation on the derived category of a differential graded algebra is induced by a morphism of differential graded algebras. Finally we discuss the relation between realisability of modules over the group cohomology ring and the Tate cohomology ring." @default.
- W76883030 created "2016-06-24" @default.
- W76883030 creator A5051741735 @default.
- W76883030 date "2007-07-08" @default.
- W76883030 modified "2023-09-27" @default.
- W76883030 title "Realisability and Localisation" @default.
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