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- W4308482081 abstract "Let $Gamma$ be a countable abelian group. An (abstract) $Gamma$-system $mathrm{X}$ - that is, an (abstract) probability space equipped with an (abstract) probability-preserving action of $Gamma$ - is said to be a Conze-Lesigne system if it is equal to its second Host-Kra-Ziegler factor $mathrm{Z}^2(mathrm{X})$. The main result of this paper is a structural description of such Conze-Lesigne systems for arbitrary countable abelian $Gamma$, namely that they are the inverse limit of translational systems $G_n/Lambda_n$ arising from locally compact nilpotent groups $G_n$ of nilpotency class $2$, quotiented by a lattice $Lambda_n$. Results of this type were previously known when $Gamma$ was finitely generated, or the product of cyclic groups. In a companion paper, two of us will apply this structure theorem to obtain an inverse theorem for the Gowers $U^3(G)$ norm for arbitrary finite abelian groups $G$." @default.
- W4308482081 created "2022-11-12" @default.
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- W4308482081 creator A5071535081 @default.
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- W4308482081 date "2021-12-03" @default.
- W4308482081 modified "2023-09-26" @default.
- W4308482081 title "The structure of arbitrary Conze-Lesigne systems" @default.
- W4308482081 doi "https://doi.org/10.48550/arxiv.2112.02056" @default.
- W4308482081 hasPublicationYear "2021" @default.
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