41 citations · 101 across the 23 of their papers we have counts for
7 papers · 1 filter
Involutions of Azumaya algebras
Uriya A. First, Ben Williams
We consider the general circumstance of an Azumaya algebra of degree over a locally ringed topos where the latter carries a (pos…
Prime decomposition for the index of a Brauer class
Benjamin Antieau, Ben Williams
We prove that the index of a Brauer class satisfies prime decomposition over a general base scheme. This contrasts with our previous result that there is no general prime decomposi…
Azumaya Algebras Without Involution
Asher Auel, Uriya A. First, Ben Williams
Generalizing a theorem of Albert, Saltman showed that an Azumaya algebra over a ring represents a -torsion class in the Brauer group if and only if there is an algebra …
The prime divisors of the period and index of a Brauer class
Benjamin Antieau, Ben Williams
We show that in locally-ringed connected topoi the primes dividing the period and index of a Brauer class coincide. The result applies in particular to Brauer classes on connected…
Topology and purity for torsors
Benjamin Antieau, Ben Williams
We study the homotopy theory of the classifying space of the complex projective linear groups to prove that purity fails for -torsors on regular noetherian schemes when …
Unramified division algebras do not always contain Azumaya maximal orders
Benjamin Antieau, Ben Williams
We show that, in general, over a regular integral noetherian affine scheme X of dimension at least 6, there exist Brauer classes on X for which the associated division algebras ove…
Serre-Godeaux varieties and the etale index
Benjamin Antieau, Ben Williams
We use the Serre-Godeaux varieties of finite groups, projective representation theory, the twisted Atiyah-Segal completion theorem, and our previous work on the topological period-…