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math.AG2025
The geometric Merkurjev-Panin Conjecture for the Cox category
Daniel Erman, Andrew Hanlon, Gaku Liu +1
We show that a strong version of the geometric Merkurjev-Panin conjecture holds for the Cox category of a projective toric variety. That is, we prove that the full strong exception…
math.AG2025
King's Conjecture and the Cox category
Matthew R. Ballard, Christine Berkesch, Michael K. Brown +6
We state and prove a realization of King's Conjecture for a category glued from the derived categories of all of the toric varieties arising from a given Cox ring. Our perspective…
math.AG2025
Computing weighted sheaf cohomology using noncommutative differential modules
Michael K. Brown, Daniel Erman
We describe a novel method for computing sheaf cohomology over weighted projective spaces and stacks using exterior algebra and differential module techniques, generalizing an algo…