Translation of Jean-Pierre Serre's 1987 letter to Tate, later published as part of 'Two letters on quaternions and modular forms (mod p)'
J-P. Serre (translated by A. Ghitza)
Israel Journal of Mathematics, No. 95 (1996).
This is an English translation of Jean-Pierre Serre's letter to Tate from 7 August 1987, describing a correspondence between the Hecke structure of modular forms (mod $p$) and quaternion algebras.