Beilinson's height pairing vs Neron-Tate - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T22:08:01Z http://mathoverflow.net/feeds/question/61620 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/61620/beilinsons-height-pairing-vs-neron-tate Beilinson's height pairing vs Neron-Tate Andreas Holmstrom 2011-04-14T01:46:48Z 2011-04-14T03:01:11Z <p>In the literature there are several different definitions of what is often referred to as Beilinson's height pairing (see for example section 4.3.8 of Gillet and Soulé's paper <a href="http://www.numdam.org/numdam-bin/fitem?id=PMIHES_1990__72__93_0" rel="nofollow">Arithmetic intersection theory</a>, and this <a href="http://hodge.mathematik.uni-mainz.de/~stefan/papers/cime.pdf" rel="nofollow">note</a> of Müller-Stach). The height pairing is supposed to generalize the <a href="http://en.wikipedia.org/wiki/Neron%25E2%2580%2593Tate_height" rel="nofollow">Neron-Tate height pairing</a>. Is there a precise statement in the literature where Beilinson's height pairing for an elliptic curve over \$\mathbb{Q}\$ is compared to the Neron-Tate pairing? </p> http://mathoverflow.net/questions/61620/beilinsons-height-pairing-vs-neron-tate/61636#61636 Answer by SGP for Beilinson's height pairing vs Neron-Tate SGP 2011-04-14T03:01:11Z 2011-04-14T03:01:11Z <p><a href="http://www.ams.org/publications/online-books/conm67-conm67-ch1.pdf" rel="nofollow">Beilinson's original paper on Height pairings</a> does indicate how his height pairing generalises that of Neron-Tate: see page 10 (also, Muller-Stach and Kunneman's works expand on Remark 4.0.8 on page 14). Also, <a href="http://www.dpmms.cam.ac.uk/~ajs1005/preprints/height-all.pdf" rel="nofollow">Scholl's paper</a> provides a very nice interpretation (via Ext in mixed motives). </p>