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# Mathematical Research Letters

## Volume 24 (2017)

### Number 4

### Perverse Nori motives

Pages: 1097 – 1131

DOI: http://dx.doi.org/10.4310/MRL.2017.v24.n4.a8

#### Author

#### Abstract

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 $k$.

Received 15 March 2015

Published 9 November 2017