Publications
Period-index bounds for arithmetic threefolds, with Benjamin Antieau, Asher Auel, Colin Ingalls and Max Lieblich,
to appear in Inventiones Mathematicae
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves, with Dan Boneh, Darren Glass, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi and Mark Zhandry,
to appear in MathCrypt 2018
Local-global Galois theory of arithmetic function fields, with David Harbater, Julia Hartmann, R. Parimala and V. Suresh,
to appear in the Israel Journal of Mathematics
Derived categories for torsors for Abelian schemes, with Benjamin Antieau and Matthew Ward,
Advances in Mathematics, 306 (2017), 1--23
Period and index, symbol lengths, and generic splittings in Galois cohomology,
Bulletin of the London Mathematical Society, 48 (2016), no. 6, 985--1000
Local-global principles for torsors over arithmetic curves, with David Harbater and Julia Hartmann,
American Journal of Mathematics, 137 (2015), no. 6, 1559--1612
Diophantine and cohomological dimensions, with Eliyahu Matzri,
Proceedings of the AMS, 143 (2015), no. 7, 2779--2788
Refinements to patching and applications to field invariants, with David Harbater and Julia Hartmann,
International Math. Research Notices, doi: 10.1093/imrn/rnu278 (2015)
Local-global principles for Galois cohomology, with David Harbater and Julia Hartmann,
Comment. Math. Helv., 89 (2014), no. 1, 215--253
Weierstrass preparation and algebraic invariants, with David Harbater and Julia Hartmann,
Math. Ann., 356 (2013), no. 4, 1405--1424
Relative Brauer groups of genus 1 curves, with Mirela Ciperiani,
Israel J. Math., 192 (2012), no. 2, 921--949
Appendix to: Period and index in the Brauer group of an arithmetic surface
By Max Lieblich,
,
J. Reine Angew. Math., 659 (2011), 1--41
Patching subfields of division algebras, with David Harbater and Julia Hartmann,
Trans. Amer. Math. Soc., 363 (2011), no. 6, 3335--3349
Distinguishing division algebras by finite splitting fields, with Kelly McKinnie,
Manuscripta Math., 134 (2011), no. 1-2, 171--182
Field patching, factorization, and local-global principles,
Quadratic forms, linear algebraic groups, and cohomology, 57--82, Dev. Math., 18, Springer, New York, 2010
Corestrictions of algebras and splitting fields,
Trans. Amer. Math. Soc., 362 (2010), no. 9, 4781--4792
Zero cycles on homogeneous varieties,
Adv. Math., 223 (2010), no. 6, 2022--2048
Applications of patching to quadratic forms and central simple algebras, with David Harbater and Julia Hartmann,
Invent. Math., 178 (2010), no. 2, 231--263
Pointed trees of projective spaces., with Linda Chen and Angela Gibney,
J. Algebraic Geom., 18 (2009), no. 3, 477--509
Index reduction for Brauer classes via stable sheaves, with Max Lieblich,
Int. Math. Res. Not. IMRN, no. 8 (2008), Art. ID rnn010, 31 pp
Birational maps between generalized Severi-Brauer varieties,
J. Pure Appl. Algebra, 212 (2008), no. 4, 689--703
Motives of unitary and orthogonal homogeneous varieties,
J. Algebra, 318 (2007), no. 1, 135--139
Severi-Brauer varieties and symmetric powers, with David J. Saltman,
Algebraic transformation groups and algebraic varieties, 59--70, Encyclopaedia Math. Sci., 132, Springer, Berlin, 2004
Severi-Brauer varieties of semidirect product algebras,
Doc. Math., 8 (2003), 527--546 (electronic)