Irreducible smooth representations of GL2(F) over characteristic p fields, where F is a finite extension of Qp, are classified up to supersingular representations. Understanding supersingular representations of GL2(Qp) was one of the first steps towards the mod p and p-adic local Langlands correspondence for GL2(Qp). However, the study of supersingular representations becomes more difficult when we change Qp to general F. In this talk, I will talk about a negative result that supersingular representations of GL2(F) are not of finite presentation whenever F is not Qp.