ON THE KERNEL OF THE BRAUER-MANIN PAIRING
Langue
en
Article de revue
Ce document a été publié dans
Journal of Number Theory. 2022, vol. 238, p. 444-463
Elsevier
Résumé en anglais
Let X be a regular scheme, flat and proper over the ring of integers of a p-adic field, with generic fiber X and special fiber X_s. We study the left kernel Br(X) of the Brauer-Manin pairing Br(X)×CH 0 (X) → Q/Z. Our main ...Lire la suite >
Let X be a regular scheme, flat and proper over the ring of integers of a p-adic field, with generic fiber X and special fiber X_s. We study the left kernel Br(X) of the Brauer-Manin pairing Br(X)×CH 0 (X) → Q/Z. Our main result is that the kernel of the reduction map Br(X) → Br(X_s) is the direct sum of (Q/Z[1/p])^s⊕(Q/Z)^t and a finite p-group, where s+t=ρ_{X_s}−ρ_X−I+1, for ρ_{X_s} and ρ_X the Picard numbers of X_s and X, and I the number of irreducible components of X_s. Moreover, we show that t>0 implies s>0.< Réduire
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