Why would anyone think that Zeref is dead? My question is a spoiler itself, you are required to be in/past Alvarez arc.


   Why would anyone think that Zeref is dead? He is right there in Alvarez a king as obvious as the sun, so how could the people in Ishgar seriously miss such a fact?


Put simply, that's all I want to know. Many people thought he was dead, others that he was simply dormant because of his low profile. 


   But we know that Zeref said that he wasn't dormant at all himself. So why would people even think that? He was right there all along in Alvarez
Zeref Dragneel is 400+ years old, very few people know him and fewer than that who know his face or has seen him.

In Chapter 208: Death Preying, neither Elfman nor Evergreen recognize Zeref. Even Natsu doesn't remember him. Marijane seems to know a little about Zeref.




  But we know that Zeref said that he wasn't dormant at all himself.


I don't know where did you find this information but, for some years he was inactive or in sleeping state. He awaken in Tenrou Island arc when he realizes Acnologia is coming.

As for Alvarez, He is known as Emperor Spriggan.


  Zeref created this empire for the sole purpose of defeating Acnologia, obtaining Fairy Heart, and annihilating Ishgar.4 His plans regarding with Fairy Heart once captured was to relive his life with the Time Magic, Neo Eclipse. A plan the Spriggan 12 were not aware of. 


When Makarov visit Alvarez to visit the Emperor Spriggan, he get shocked seeing Zeref as Emperor. Which also shows that how little the information of Zeref is available in present world. Makarov is one of the Ten Wizard Saints.



The image is from chapter 444: Emperor Spriggan, shocking face of Makarov when he sees Zeref as Emperor.