article published yes Timothy D Browning author 35827D50-F248-11E8-B48F-1D18A9856A870000-0002-8314-0177 Daniel Loughran author TiBr department An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points. American Mathematical Society2019 eng 0002-9947 1088-6850 1705.01999 00046403420001910.1090/tran/7514 37185757-5785 Browning, Timothy D, and Daniel Loughran. “Sieving Rational Points on Varieties.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2019. <a href="https://doi.org/10.1090/tran/7514">https://doi.org/10.1090/tran/7514</a>. T. D. Browning and D. Loughran, “Sieving rational points on varieties,” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8. American Mathematical Society, pp. 5757–5785, 2019. Browning, T. D., &#38; Loughran, D. (2019). Sieving rational points on varieties. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/tran/7514">https://doi.org/10.1090/tran/7514</a> Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions of the American Mathematical Society. 371(8), 5757–5785. T.D. Browning, D. Loughran, Transactions of the American Mathematical Society 371 (2019) 5757–5785. Browning TD, Loughran D. Sieving rational points on varieties. <i>Transactions of the American Mathematical Society</i>. 2019;371(8):5757-5785. doi:<a href="https://doi.org/10.1090/tran/7514">10.1090/tran/7514</a> Browning, Timothy D., and Daniel Loughran. “Sieving Rational Points on Varieties.” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8, American Mathematical Society, 2019, pp. 5757–85, doi:<a href="https://doi.org/10.1090/tran/7514">10.1090/tran/7514</a>. 1752018-12-11T11:45:01Z2025-07-10T11:51:20Z