45 citations · 134 across the 18 of their papers we have counts for
26 papers
Equivariant Unirationality of Cubic Threefolds
Matthew Ballard, Alexander Duncan, Zhijia Zhang
Using the recent proof of the Cassels--Swinnerton-Dyer conjecture for cubic surfaces, we finish the classification of -unirational complex cubic threefolds. In particular, we pr…
Growing Mathlib: maintenance of a large scale mathematical library
Anne Baanen, Matthew Robert Ballard, Johan Commelin +3
The Lean mathematical library Mathlib is one of the fastest-growing libraries of formalised mathematics. We describe various strategies to manage this growth, while allowing for ch…
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…
High Frobenius pushforwards generate the bounded derived category
Matthew R. Ballard, Srikanth B. Iyengar, Pat Lank +2
This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme of prime characteristic. The main result is that when the Frobenius…
Consequences of the existence of exceptional collections in arithmetic and rationality
Matthew R. Ballard, Alexander Duncan, Alicia Lamarche +1
A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic…
Separable algebras and coflasque resolutions
Matthew R. Ballard, Alexander Duncan, Alicia Lamarche +1
Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects. The most famous example is the deep connect…