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The Brauer–Manin Obstruction for Zero‐Cycles on Severi–Brauer Fibrations Over Curves
Author(s) -
van Hamel Joost
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004605
Subject(s) - mathematics , brauer group , pure mathematics , fibration , zero (linguistics) , brauer's theorem on induced characters , projective variety , global field , hasse principle , variety (cybernetics) , algebraic number field , philosophy , linguistics , statistics , homotopy
Introducing the framework of pseudo‐motivic homology, the paper finishes the proof that the Brauer–Manin obstruction is the only obstruction to the local–global principle for zero‐cycles on a Severi–Brauer fibration of squarefree index over a smooth projective curve over a number field, provided that the Tate–Shafarevich group of the Jacobian of the base curve is finite. More precisely, for such a variety the Chow group of global zero‐cycles is dense in the subgroup of collections of local cycles that are orthogonal to the (cohomological) Brauer group of the variety.