| Firstly, we solve the following question proposed by Glenn Stevens. Consider which can be interpreted as a cohomology class in by local class field theory. The question is how to calculate the derivative Using Perrin-Riou's theory, we prove THEOREM 0.1 where γp denotes the Kummer class associated to p. Next, we generalize Perrin-Riou-Colmez's theory to the setting of formal groups. We construct an exponential map from to where is the Galois group of the Lubin-Tate tower associated to the formal group. We then prove its h-twist maps tempered distributions to tempered distributions and satisfies the following formula: THEOREM 0.2.* Finally, we study a two-variable family of cohomology classes. THEOREM 0.3. There is an exponential map from to which is compatible with the exponential maps in Theorem 0.2 under the quotient map Moreover, we have the following formula:* *Please refer to dissertation for formulas. |