107 citations · 173 across the 36 of their papers we have counts for
14 papers · 1 filter
Classes in of lower exponent
Adam Chapman, Daniel Krashen, Kelly McKinnie
Let be a field of characteristic . We prove that if a symbol in is of exponent dividing , then its s…
Transcendental splitting fields of division algebras
Daniel Krashen, Max Lieblich
We examine when division algebras can share common splitting fields of certain types. In particular, we show that one can find fields for which one has infinitely many Brauer class…
Local-global Galois theory of arithmetic function fields
David Harbater, Julia Hartmann, Daniel Krashen +2
We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for loc…
Refinements to patching and applications to field invariants
David Harbater, Julia Hartmann, Daniel Krashen
We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms…
Diophantine and cohomological dimensions
Daniel Krashen, Eliyahu Matzri
We give explicit linear bounds on the p-cohomological dimension of a field in terms of its Diophantine dimension. In particular, we show that for a field of Diophantine dimension a…
Period and index, symbol lengths, and generic splittings in Galois cohomology
Daniel Krashen
We use constructions of versal cohomology classes based on a new notion of "presentable functors," to describe a relationship between the problems of bounding symbol length in coho…