## Cohen-Lenstra heuristics

- Informal reading group on the Cohen-Lenstra heuristics
- chair: Bjorn Poonen
- The first meeting of the reading group was Tuesday, January 25, 11-12.
- The second meeting will be Tuesday, February 8, 11-12 in the 2nd floor seminar room if that room is available. It will focus on heuristics for Shafarevich-Tate groups.
- Reading list (in increasing order of sophistication):
- MR0750661 Cohen, H. ; Lenstra, H. W., Jr. Heuristics on class groups. Number theory (New York, 1982), 26--36, Lecture Notes in Math., 1052, Springer, Berlin, 1984.
- MR0756082 (85j:11144) Cohen, H. ; Lenstra, H. W., Jr. Heuristics on class groups of number fields. Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983), 33--62, Lecture Notes in Math., 1068, Springer, Berlin, 1984.
- MR1837670 (2003a:11065) Delaunay, Christophe. Heuristics on Tate-Shafarevitch groups of elliptic curves defined over Q. Experiment. Math. 10 (2001), no. 2, 191--196.
Delaunay, Christophe. Formes modulaire et invariants de courbes elliptiques définies sur Q. Thèse, Université Bordeaux I, 2002.

PDFs of these have been placed in Poonen's public directory at MSRI. Type

`cd ~bpoonen/Public`at a terminal prompt.Melanie Wood points out that the paper [Friedman, Eduardo; Washington, Lawrence C. On the distribution of divisor class groups of curves over a finite field. Theorie des nombres (Quebec, PQ, 1987), 227-239, de Gruyter, Berlin, 1989] does one of the projects suggested at the Jan. 25 meeting, to show that the distribution on the cokernel of a random matrix in M_n(Z_p) tends as n-->infinity to the distribution of the p-part of a random abelian group according to the Cohen-Lenstra measure. She also mentions http://www.math.ucla.edu/~maples/maples-cokernel.pdf, which shows that the same distribution is obtained for nearly every coefficient distribution.