Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
Siddharth Mathur, University of Arizona
"Azumaya Algebras and the Resolution Property"
Azumaya algebras, are (etale) twisted forms of matrix rings. These objects are of great utility because they give rise to Brauer classes. Fifty years ago, Grothendieck asked whether every cohomological Brauer class has a corresponding Azumaya algebra. This question is still open even for smooth separated threefolds over the complex numbers!
One says a scheme (or Algebraic stack) X satisfies the resolution property if every coherent sheaf is the quotient of a vector bundle. The work of Totaro and Gross explains that this property holds iff X admits a very special quotient stack presentation. However, whether or not separated Algebraic stacks have this property remains a difficult question.
The goal of our talk will be to explain
(1) Why these two questions are deeply intertwined,
(2) New results regarding the existence of Azumaya Algebras and
(3) How we can use results as in (2) to show large classes of algebraic stacks satisfy the resolution property.
MC 5403
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.