Geodesic
The reciprocity obstruction for rational points on compactifications of torsors under tori over fields with global duality
Documenta mathematica, Tome 8 (2003), pp. 125-142.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper studies the reciprocity obstruction to the local--global principle for compactifications of torsors under tori over a generalised global field of characteristic zero. Under a non-divisibility condition on the second Tate--Shafarevich group for tori, it is shown that the reciprocity obstruction is the only obstruction to the local--global principle. This gives in particular an elegant unified proof of Sansuc's result on the Brauer--Manin obstruction for compactifications of torsors under tori over number fields, and Scheiderer's result on the reciprocity obstruction for compactifications of torsors under tori over $p$-adic function fields.
Classification : 14G25, 11G35, 14F20, 11E72
Keywords: arithmetic algebraic geometry, Diophantine geometry, varieties over global fields, Brauer--Manin obstruction, homogeneous spaces over global fields 
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     author = {van Hamel, Joost},
     title = {The reciprocity obstruction for rational points on compactifications of torsors under tori over fields with global duality},
     journal = {Documenta mathematica},
     pages = {125--142},
     publisher = {mathdoc},
     volume = {8},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a11/}
}
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van Hamel, Joost. The reciprocity obstruction for rational points on compactifications of torsors under tori over fields with global duality. Documenta mathematica, Tome 8 (2003), pp. 125-142. http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a11/