Arithmetic in the Boij-Söderberg Cone and Betti Number Conjectures
Published:Dec 30, 2025 16:17
•1 min read
•ArXiv
Analysis
This paper addresses long-standing conjectures about lower bounds for Betti numbers in commutative algebra. It reframes these conjectures as arithmetic problems within the Boij-Söderberg cone, using number-theoretic methods to prove new cases, particularly for Gorenstein algebras in codimensions five and six. The approach connects commutative algebra with Diophantine equations, offering a novel perspective on these classical problems.
Key Takeaways
- •Proves new cases of conjectures about Betti numbers in codimensions five and six.
- •Reframes the conjectures as arithmetic problems within the Boij-Söderberg cone.
- •Utilizes number-theoretic methods and Diophantine equations to analyze the problem.
- •Provides a novel connection between commutative algebra and number theory.
Reference
“Using number-theoretic methods, we completely classify these obstructions in the codimension three case revealing some delicate connections between Betti tables, commutative algebra and classical Diophantine equations.”