Publications

Relative Brauer groups of genus 1 curves, with Mirela Ciperiani,
to appear in the Israel Journal of Mathematics,
(arxiv)
Distinguishing algebras by their finite splitting fields, with Kelly McKinnie,
to appear in Manuscripta Mathematica,
(arxiv)
Corestrictions of algebras and splitting fields,
to appear in Transactions of the American Mathematical Society,
(arxiv)
Appendix to : Period and index in the Brauer group of an arithmetic surface, by Max Lieblich,
to appear in Journal für die reine und angewandte Mathematik (Crelle's Journal),
(arxiv)
Patching subfields of division algebras, with David Harbater and Julia Hartmann,
to appear in Transactions of the American Mathematical Society,
(arxiv)
Field patching, factorization and local-global principles,
in the book Quadratic forms, linear algebraic groups, and cohomology, Developments in Mathematics, Vol 18, pp. 57–82, Springer, 2010, ISBN 978-1-4419-6210-2.
(arxiv, Springer, Amazon)
Zero cycles on homogeneous varieties,
Advances in Mathematics, Vol. 223, 2010, no. 6, pp. 2022–2048
(arxiv, journal)
Applications of patching to quadratic forms and central simple algebras, with David Harbater and Julia Hartmann,
Inventiones Mathematica, SpringerLink Date April 21, 2009.
(arxiv, journal)
Pointed trees of projective spaces, with Linda Chen and Angela Gibney,
Journal of Algebraic Geometry, Vol. 18, Number 3, July 2009.
(arxiv)
Index reduction for Brauer classes via stable sheaves, with Max Lieblich, appendix by Bhargav Bhatt,
International Math. Research Notices, 2008, Vol. 2008, article ID: rnn010-31.
(arxiv)
Birational maps between generalized Severi-Brauer varieties,
Journal of Pure and Applied Algebra, Vol. 212, 2008, Number 4, pp. 689–703.
(arxiv)
Motives of unitary and orthogonal homogeneous varieties,
Journal Algebra, Vol. 318/1, pp. 135–139, 2007.
(arxiv, journal)
Severi-Brauer Varieties and Symmetric Powers, with David Saltman,
in the book Invariant Theory and Algebraic Transformation Groups, Encyclopaedia of Mathematical Sciences, Vol. 132, Springer-Verlag 2004.
(Springer, Amazon)
Severi-Brauer varieties of semidirect product algebras,
Documenta Mathematica, Vol. 8, 2003, pp 527–546.
(arxiv, journal)

Preprints

Weierstrass preparation and algebraic invariants, with David Harbater and Julia Hartmann,
submitted for publication.
(arxiv)
Local-global principles for torsors over arithmetic curves, with David Harbater and Julia Hartmann,
submitted for publication.
(arxiv)

Other Manuscripts

Birational isomorphisms between Severi-Brauer varieties,
PhD Thesis, University of Texas at Austin, 2001.
(pdf)
Moduli of étale subalgebras in a central simpla algebra,
(much of this material has been subsumed in the above paper "Zero cycles on homogeneous varieties").
(arxiv)
Quadratic forms and the period-index problem,
This note describes elementary consequences of some deep results in the theory of quadratic forms to the period-index problem for cohomology classes.
(pdf)

Lecture Slides

Local global principles for field patching and applications to quadratic forms and division algebras,
(pdf)