9 citations · 9 across the 10 of their papers we have counts for
12 papers
Refined index obstructions for Brauer classes on an abelian variety
Eoin Mackall
We produce refined index obstructions, generalizing recently constructed index obstructions due to de Jong and Perry, for topologically trivial Brauer classes on smooth and project…
An algorithmic reduction to canonical forms for vector bundles on anisotropic conics
Eoin Mackall, Diego Yépez
We describe a polynomial complexity algorithm for reducing transition matrices, for vector bundles glued along a clutching-type cover of a real anisotropic conic, to canonical bloc…
A Looming of phantoms
Kimoi Kemboi, Daniel Krashen, Tianle Liu +6
Following Krah's method, we construct new examples of phantom categories as semiorthogonal components of the derived categories of two types of rational surfaces: the blowup of the…
On deformations of Azumaya algebras with quadratic pair
Eoin Mackall, Cameron Ruether
We construct a tangent-obstruction theory for Azumaya algebras equipped with a quadratic pair. Under the assumption that either 2 is a global unit or the algebra is of degree 2, we…
On the algebraizability of formal deformations in -cohomology
Eoin Mackall
We show that algebraizability of the functors and is a stable birational invariant for smooth and proper varieties $π:X\righ…
Elliptic curves and their principal homogeneous spaces: splitting Severi--Brauer varieties
Eoin Mackall, Nick Rekuski
We consider the question: which elliptic curves appear as the Jacobian of a smooth curve of genus one splitting a Severi--Brauer variety? We provide three new examples. First, we s…
Pro-representability of -cohomology in weight 3 generalizing a result of Bloch
Eoin Mackall
We generalize a result, on the pro-representability of Milnor -cohomology groups at the identity, that's due to Bloch. In particular, we prove, for a smooth, proper, and geo…
On the Chow groups of a biquaternion Severi--Brauer variety
Eoin Mackall
We provide an alternative proof that the Chow group of -cycles on a Severi--Brauer variety associated to a biquaternion division algebra is torsion-free. There are three proofs…
The Period and Index of a Generic Geometrically Elliptic Normal Curve
Eoin Mackall
We construct genus one curves on base extensions of generic Severi--Brauer varieties of a given index and period which are versal objects for families of geometrically elliptic nor…
-homotopy equivalences and a theorem of Whitehead
Eoin Mackall
We prove analogs of Whitehead's theorem (from algebraic topology) for both the Chow groups and for the Grothendieck group of coherent sheaves: a morphism between smooth projective…
Universal additive Chern classes and a GRR-type theorem
Eoin Mackall
We construct a functor, from the category of schemes to the category of graded rings, that is an initial object for having a theory of Chern classes with an additive first Chern cl…
Six variations on a theme: almost planar graphs
Max Lipton, Eoin Mackall, Thomas W. Mattman +4
A graph is apex if it can be made planar by deleting a vertex, that is, such that is planar. We define the related notions of edge apex, such that $G-…