A note on extensions of multilinear maps defined on multilinear varieties

DOI10.1017/S0013091521000055zbMath1472.11273arXiv1906.04807OpenAlexW3159371212MaRDI QIDQ4999881

Luka Milićević, Timothy Gowers

Publication date: 5 July 2021

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.04807

zbMATH Keywords

extensions of mapsmultilinear mapsmultilinear varieties

Mathematics Subject Classification ID

Additive number theory; partitions (11P99) Arithmetic combinatorics; higher degree uniformity (11B30) Combinatorial aspects of algebraic geometry (05E14)

Cites Work

• Linear forms and higher-degree uniformity for functions on \(\mathbb F^n_p\)
• A bilinear Bogolyubov theorem
• The partition rank of a tensor and \(k\)-right corners in \(\mathbb{F}_q^n\)
• Properties of high rank subvarieties of affine spaces
• Polynomial bound for partition rank in terms of analytic rank
• A bilinear version of Bogolyubov’s theorem
• Polynomial bound for the partition rank vs the analytic rank of tensors
• A note on the bilinear Bogolyubov theorem: Transverse and bilinear sets
• The analytic rank of tensors and its applications
• A bilinear Bogolyubov-Ruzsa lemma with poly-logarithmic bounds

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