Principe local-global pour les zéro-cycles

Abstract : This Ph. D. thesis studies the arithmetic properties (the Hasse principle, the weak approximation, and the Brauer-Manin obstruction) for zero-cycles on algebraic varieties defined over number fields. We introduce the notion of generalized Hilbertian subset. By using the fibration method, we prove that the Brauer-Manin obstruction is the only obstruction tothe Hasse principle and to the weak approximation for zero-cycles of degree 1; and establish the exactness of a sequence of global-local type concerning Chow groups of zero-cycles, for certain varieties which admit a fibration structure overa smooth curve or over the projective space, where the arithmetic hypotheses are only posed on the fibers over a generalized Hilbertian subset. Moreover, we relate the arithmetic of rational points and that of zero-cycles of degree 1 on geometrically rationally connected varieties. As an application, we find that the Brauer-Manin obstruction is the only obstruction to the Hasse principle and to the weak approximation for zero-cycles of degree 1 on- homogeneous spaces of a linear algebraic group with connected stabilizer,- certain varieties fibered into Chatelet surfaces over a smooth curve or over the projective space (in particular, Poonen's threefolds).
Document type :
Theses
Complete list of metadatas

Cited literature [40 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00630560
Contributor : Abes Star <>
Submitted on : Monday, October 10, 2011 - 2:02:17 PM
Last modification on : Friday, May 17, 2019 - 10:39:43 AM
Long-term archiving on : Wednesday, January 11, 2012 - 2:23:33 AM

File

VA_LIANG_YONGQI_04102011.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-00630560, version 1

Collections

Citation

Yongqi Liang. Principe local-global pour les zéro-cycles. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2011. Français. ⟨NNT : 2011PA112190⟩. ⟨tel-00630560⟩

Share

Metrics

Record views

881

Files downloads

398