Perverse Nori motives

Let $k = \mathbb{C}$ be the field of complex numbers (one can also choose a field of characteristic zero $k$ with a fixed embedding of fields $\sigma : k \hookrightarrow \mathbb{C})$. Assume that $K$ is a field. In this work, we show that the Tannakian formalism developed by M. Nori also applies to representations $\mathsf{T} : \mathcal{Q} \to \mathscr{P}$ with values in a $K$-linear Abelian category $\mathscr{P}$ which is Noetherian, Artinian and has finite dimensional Hom groups over $K$. As an application, we define a relative version, modeled after perverse sheaves, of the Abelian category of motives constructed by M. Nori over $k$.

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Received 15 March 2015

Accepted 23 November 2015

Published 9 November 2017