Rational Points on Homogeneous Varieties and Equidistribution of Adelic Periods |
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Authors: | Alex Gorodnik Hee Oh Mikhail Borovoi |
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Institution: | 1. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK 2. Mathematics department, Brown University, Providence, RI, USA 3. Korea Institute for Advanced Study, Seoul, Korea 4. School of Mathematical Sciences, Sackler Faculty of Exact Science, Tel Aviv University, 69978, Tel Aviv, Israel
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Abstract: | Let U := L\G be a homogeneous variety defined over a number field K, where G is a connected semisimple K-group and L is a connected maximal semisimple K-subgroup of G with finite index in its normalizer. Assuming that G(K
v
) acts transitively on U(K
v
) for almost all places v of K, we obtain an asymptotic for the number of rational points U(K) with height bounded by T as T → ∞, and settle new cases of Manin’s conjecture for many wonderful varieties. The main ingredient of our approach is the
equidistribution of semisimple adelic periods, which is established using the theory of unipotent flows. |
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Keywords: | |
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