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This is a Quantitative Study study.

October 1, 20250 citationsOpen Access

Integral Artin motives II: Perverse motives and Artin Vanishing Theorem

Key Points

The study shows that perverse motivic t-structures can exist on Artin motives in low dimensions.
It demonstrates a homotopy t-structure approximation for Artin motives with rational coefficients.
The heart of the constructed t-structure mimics aspects of the perverse sheaves category.
Key findings include the non-existence of the perverse t-structure in dimension four.

Abstract

In this text, we are mainly interested in the existence of the perverse motivic t-structures on the category of Artin \'etale motives with integral coefficients. We construct the perverse homotopy t-structure which is the best possible approximation to a perverse t-structure on Artin motives with rational coefficients. The heart of this t-structure has properties similar to those of the category of perverse sheaves and contains the Ayoub-Zucker motive. With integral coefficients, we construct the perverse motivic t-structure on Artin motives when the base scheme is of dimension at most 2 and show that it cannot exist in dimension 4. This construction relies notably on a an analogue for Artin motives of the Artin Vanishing Theorem.

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