Highest Weight Categories For Number Rings
Annette Pilkington
TL;DR
This paper establishes that certain categories associated with number rings and Galois groups are highest weight categories by proving BGG reciprocity and duality, linking their structure to ramification properties.
Contribution
It introduces the concept of stratified exact categories for number rings and proves they are highest weight categories, connecting algebraic structure with ramification.
Findings
BGG reciprocity holds for these categories
Duality is established within the categories
Structure of categories relates to ramification in number rings
Abstract
This paper examines the concept of a stratified exact category in the context of number rings and corresponding Galois groups. BGG reciprocity and duality are proven for these categories making them highest weight categories. The strong connections between the structure of the category and ramification in the ring are explored.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications