Graded and Filtered Fiber Functors on Tannakian Categories
Paul Ziegler
TL;DR
This paper investigates fiber functors with grading or filtration structures on Tannakian categories, establishing foundational results and showing filtrations can be locally split by gradings in the fpqc topology.
Contribution
It provides a comprehensive foundation for graded and filtered fiber functors, proving filtrations can be locally split by gradings on the base scheme.
Findings
Filtrations on fiber functors can be split by gradings fpqc-locally.
Establishes foundational results for graded and filtered fiber functors.
Provides a framework for understanding fiber functors with additional structures.
Abstract
We study fiber functors on Tannakian categories which are equipped with a grading or a filtration. Our goal is to give a comprehensive set of foundational results about such functors. A main result is that each filtration on a fiber functor can be split by a grading fpqc-locally on the base scheme.
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