Local Rigidity and Six Functor Formalisms

Adrian Clough

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arXiv · 2408.07564

Local Rigidity and Six Functor Formalisms

Adrian Clough

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Abstract

The coefficient categories of six functor formalisms are often locally rigid, and when this is the case, the exceptional pushforward and pullback adjunctions may be defined formally. In this short note it is shown that for f a proper map resp. an open embedding the well known formulas f_! = f_* resp. f_! = f_# may likewise be deduced formally.

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Adrian Clough. 2024-08-14. Local Rigidity and Six Functor Formalisms. https://arxiv.org/abs/2408.07564

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