Editing Sato–Tate conjecture (section)

==Generalisations==
There are generalisations, involving the distribution of [[Frobenius element]]s in [[Galois group]]s involved in the [[Galois representation]]s on [[étale cohomology]]. In particular there is a conjectural theory for curves of genus&nbsp;''n''&nbsp;>&nbsp;1.

Under the random matrix model developed by [[Nick Katz]] and [[Peter Sarnak]],<ref>{{Citation |title=Random matrices, Frobenius Eigenvalues, and Monodromy |first1=Nicholas M. |last1=Katz |name-list-style=amp |first2=Peter |last2=Sarnak |location=Providence, RI |publisher=American Mathematical Society |year=1999 |isbn=978-0-8218-1017-0 }}</ref> there is a conjectural correspondence between (unitarized) characteristic polynomials of Frobenius elements and [[conjugacy class]]es in the [[compact Lie group]] USp(2''n'')&nbsp;=&nbsp;[[Sp(n)|Sp(''n'')]].  The [[Haar measure]] on USp(2''n'') then gives the conjectured distribution, and the classical case is USp(2)&nbsp;=&nbsp;[[SU(2)]].