A finite field is a specific model of the Euclidean space and closely related to problems in other fields such as the additive number theory, combinatorics and algebraic geometry.
For these reasons, Mockenhaupt and Tao introduced the restriction problem in finite field setting. This topic has been extensively studied over the last years.
In this talk, we consider the restriction estimate for the cone over a finite field, which gives the sharp results in a four dimensional case.
Moreover we introduce an approach to study incidence problems using the cone restriction estimates.