My boyfriend of 4 years broke up with me because I'm jealous that he is still in touch with his ex-girlfriend. They have contact only through email, she talks about meeting up for drinks with him but he never goes. Now he broke up with me because he says he can't take it anymore.

How do I stop the nonsense and win him back. I love him and I miss him terribly.

Well, if you really loved him you would have trusted him.
You said you were jealous that he was in contact with his ex-gf, but I have a feeling what you mean by that was you were scared he would leave you for her, or maybe even cheat on you with her.
You need to tell him that you trust him when he talks to any girl because you love him.

And frankly, I was kind of taken back when you said "How do I stop the nonsence and win him back?" Love isn't something you win. You are not in compatition with her. If you are meant to be together you shouldn't have to win a battle to get him back.

My boyfriend of 4 years broke up with me because I'm jealous that he is still in touch with his ex-girlfriend. They have contact only through email, she talks about meeting up for drinks with him but he never goes. Now he broke up with me because he says he can't take it anymore.

How do I stop the nonsense and win him back. I love him and I miss him terribly.
Thank you so much mjl for your insightful answer. You are absolutely right, love equals trust and I was thinking that maybe there could be a chance for them instead of saying to myself he's with me, not her. You are also right when you say that it isn't a competition. I believe that I was making it just that.

Now I need to think about how to show him that I trust him and that I do love him with all my heart. It's a tough thing to do when we are barely talking now. I know it will take time, I'm just worried that when I do change he won't see it.

You are right, it will take time. And I'm glad you understand my post.
Just remember whether you are dating a person that talks to their ex or not, a relationship is all about trust. Without trust, your relationship won't last.
Good luck with everything.