Rational points on compactifications of semi-simple groups

Shalika, Joseph¹ ; Takloo-Bighash, Ramin² ; Tschinkel, Yuri^3, 4

¹ Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218-2686
² Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
³ Courant Institute, NYU, 251 Mercer Street, New York, New York 10012
⁴ Mathematisches Institut, Bunsenstr. 3-5, 37073 Göttingen, Germany

Journal of the American Mathematical Society, Tome 20 (2007) no. 4, pp. 1135-1186

Résumé

We prove Manin’s conjecture concerning the distribution of rational points of bounded height, and its refinement by Peyre, for wonderful compactifications of semi-simple algebraic groups over number fields. The proof proceeds via the study of the associated height zeta function and its spectral expansion.

Détail

DOI : 10.1090/S0894-0347-07-00572-3

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