In this talk we will be interested in some properties of the Galois cohomology groups of function fields, with torsion coefficients. We will discuss questions on the ramification of the elements of these groups, as well as one local-global principle if K is the function field of a surface over a finite field. This local-global principle is due to Parimala and Suresh and is important for the study of quadratic forms and, more precisely, the u-invariant. We will show how to extend this principle in case when there are so-called ´hot points´ in Saltman´s classification and also provide a motivation coming from questions on quadratic forms.