HELP!!!! SAMSUNG GALAXY S4 COMPATIBILITY????

Hi guys, I need help regarding Samsung Galaxy S4's Network compatibility. I live in Mexico, the only decent carrier here is called TELCEL, I have an Iphone 5 right now and always want the latest phone, SICK of Apple, I fell in love with Android so I bought the new HTC One Unlocked from a dealer in UK, when I got it here, to my surprise, when inserted my iphone 5's LTE nano chip into the HTC One (using a sim adapter of course) IT DIDNT WORK, NEVER GOT A SIGNAL AT ALL, after some research I realized the HTC One would never work in Mexico because of the NETWORK COMPATIBILITY, now I am stuck with an expensive phone and no use for it.

Now I wanna buy an Unlocked Galaxy S4 but wont make the same mistake again!!!! That's why I need you experts in the whole Network and channel bands subject to HELP ME, be sure if an UNLOCKED, SAMSUNG GALAXY S4 will work with my sim card in MEXICO.

THANK YOU SO MUCH!!!!