The period-index problem for the Brauer group of an algebraic surface

By A. J. Jong. 2004

147 citations recorded by the source corpus.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/caba15fdabea421205435cc6dafe0e92dcc81389

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In Applied Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Twisted sheaves and the period-index problem (2005, methodology): “n construct an unobstructed locally free twisted sheaf of the desired rank using strict transforms (see e.g. 5.2.5 and 5.2.6 of [23] for the untwisted version, [34] for the twisted version, or 3.2 of [12] for a treatment in terms of Azumaya algebras). Deforming it over the total space of X yields th”
The topological period–index problem over 6‐complexes (2012, background): “The conjecture has been proved in the case of d = 2 by de Jong [17], but is not known for any higher-dimensional varieties, not even for P3.”
Lectures on K3 Surfaces (2016, methodology): “For function fields of surfaces and for surfaces over finite fields this has been addressed by de Jong [135] and Lieblich [364].”
Applications of patching to quadratic forms and central simple algebras (2008, background): “Then the Brauer dimension of k is 1 by [6].”
Open problems on central simple algebras (2010, background): “ults on division algebras over the function ﬁeld of a p-adic curve, see [Sal97a], [Sal07], [Bru10], [PS98], [PSar]; De Jong’s result on the Brauer group of the function ﬁeld of a complex surface, see [dJ04], [Lie08], and §4; Harbater–Hartmann–Krashenpatchingtechniques, see[HHK09]and [HHKar]; and Mer”
Period and index in the Brauer group of an arithmetic surface (2007, methodology): “ve over an algebraically closed ﬁeld is trivial. (More generally, his proof shows that any C 1-ﬁeld has trivial Brauer group.) The next progress in this direction was not made until de Jong proved in [10] that the period and index are equal for Brauer classes over the function ﬁeld of a surface over”