Non-abelian Mellin transformations and applications. (16th November 2022)

• Record Type: Journal Article
• Authors: Liu, Yongqiang; Maxim, Laurenţiu; Wang, Botong
• Is Part Of: Forum of mathematics. Volume 10(2022)
• Publication Date: 2022-11-16
• Subjects: 14F35 -- 14F45 -- 14F06 -- 32S55 -- 32S60; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2022.91
• Languages: English
• ISSNs: 2050-5094

Abstract

Abstract: We study non-abelian versions of the Mellin transformations, originally introduced by Gabber-Loeser on complex affine tori. Our main result is a generalisation to the non-abelian context and with arbitrary coefficients of the t -exactness of Gabber-Loeser's Mellin transformation. As an intermediate step, we obtain vanishing results for the Sabbah specialisation functors. Our main application is to construct new examples of duality spaces in the sense of Bieri-Eckmann, generalising results of Denham-Suciu.