Crossed Burnside rings and cohomological Mackey $2$-motives

Fumihito Oda; Yugen Takegahara; Tomoyuki Yoshida

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arXiv · 2201.04744

Crossed Burnside rings and cohomological Mackey $2$-motives

Fumihito Oda·Yugen Takegahara·Tomoyuki Yoshida

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Abstract

Balmer and Dell'Ambrogio introduced the pseudo-functor $P$ from the bicategory of $k$-linear Mackey $2$-motives to the bicategory of $k$-linear cohomological Mackey $2$-motives over a commutative ring $k$. They showed that $P$ maps the general Mackey $2$-motives to the cohomological Mackey $2$-motives by using the ring homomorphism from the crossed Burnside ring of a finite group $G$ over $k$ to the center $ ZkG$ of group algebra $kG$ ([BD21, Theorem 5.3]). We study the behavior of motivic decomposition of cohomological Mackey $2$-motives as images by $P$ of motivic decomposition of Mackey $2$-motives.

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BibTeX RIS

Fumihito Oda, Yugen Takegahara, Tomoyuki Yoshida. 2022-01-13. Crossed Burnside rings and cohomological Mackey $2$-motives. https://arxiv.org/abs/2201.04744

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