Manin’s and Peyre’s conjectures on rational points and adelic mixing
Alex Gorodnik; François Maucourant; Hee Oh
Annales scientifiques de l'École Normale Supérieure (2008)
- Volume: 41, Issue: 3, page 385-437
- ISSN: 0012-9593
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topGorodnik, Alex, Maucourant, François, and Oh, Hee. "Manin’s and Peyre’s conjectures on rational points and adelic mixing." Annales scientifiques de l'École Normale Supérieure 41.3 (2008): 385-437. <http://eudml.org/doc/272104>.
@article{Gorodnik2008,
abstract = {Let $X$ be the wonderful compactification of a connected adjoint semisimple group $G$ defined over a number field $K$. We prove Manin’s conjecture on the asymptotic (as $T\rightarrow \infty $) of the number of $K$-rational points of $X$ of height less than $T$, and give an explicit construction of a measure on $X(\mathbb \{A\})$, generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points $\mathbf \{G\}(K)$ on $X(\mathbb \{A\})$. Our approach is based on the mixing property of $\{L\}^2(\mathbf \{G\}(K)\backslash \mathbf \{G\}(\mathbb \{A\}))$ which we obtain with a rate of convergence.},
author = {Gorodnik, Alex, Maucourant, François, Oh, Hee},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Rational points; Manin conjecture; algebraic groups},
language = {eng},
number = {3},
pages = {385-437},
publisher = {Société mathématique de France},
title = {Manin’s and Peyre’s conjectures on rational points and adelic mixing},
url = {http://eudml.org/doc/272104},
volume = {41},
year = {2008},
}
TY - JOUR
AU - Gorodnik, Alex
AU - Maucourant, François
AU - Oh, Hee
TI - Manin’s and Peyre’s conjectures on rational points and adelic mixing
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2008
PB - Société mathématique de France
VL - 41
IS - 3
SP - 385
EP - 437
AB - Let $X$ be the wonderful compactification of a connected adjoint semisimple group $G$ defined over a number field $K$. We prove Manin’s conjecture on the asymptotic (as $T\rightarrow \infty $) of the number of $K$-rational points of $X$ of height less than $T$, and give an explicit construction of a measure on $X(\mathbb {A})$, generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points $\mathbf {G}(K)$ on $X(\mathbb {A})$. Our approach is based on the mixing property of ${L}^2(\mathbf {G}(K)\backslash \mathbf {G}(\mathbb {A}))$ which we obtain with a rate of convergence.
LA - eng
KW - Rational points; Manin conjecture; algebraic groups
UR - http://eudml.org/doc/272104
ER -
References
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