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math.AG2021
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…
math.AG2021
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…
math.AG2021
-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…