2,463 research outputs found
Local-global principles for Galois cohomology
This paper proves local-global principles for Galois cohomology groups over
function fields of curves that are defined over a complete discretely
valued field. We show in particular that such principles hold for , for all . This is motivated by work of Kato and others, where
such principles were shown in related cases for . Using our results in
combination with cohomological invariants, we obtain local-global principles
for torsors and related algebraic structures over . Our arguments rely on
ideas from patching as well as the Bloch-Kato conjecture.Comment: 32 pages. Some changes of notation. Statement of Lemma 2.4.4
corrected. Lemma 3.3.2 strengthened and made a proposition. Some proofs
modified to fix or clarify specific points or to streamline the presentatio
Regulators of canonical extensions are torsion: the smooth divisor case
In this paper, we prove a generalization of Reznikov's theorem which says
that the Chern-Simons classes and in particular the Deligne Chern classes (in
degrees ) are torsion, of a flat bundle on a smooth complex projective
variety. We consider the case of a smooth quasi--projective variety with an
irreducible smooth divisor at infinity. We define the Chern-Simons classes of
Deligne's canonical extension of a flat vector bundle with unipotent monodromy
at infinity, which lift the Deligne Chern classes and prove that these classes
are torsion
Seeking the balance: Patching double and exceptional field theories
We investigate the patching of double and exceptional field theories. In
double field theory the patching conditions imposed on the spacetime after
solving the strong section condition imply that the 3-form field strength
is exact. A similar conclusion can be reached for the form field strengths of
exceptional field theories after some plausive assumptions are made on the
relation between the transition functions of the additional coordinates and the
patching data of the form field strengths. We illustrate the issues that arise,
and explore several alternative options which include the introduction of
C-folds and of the topological geometrisation condition.Comment: substantial changes, section with example added, to appear in jhep,
24 page
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