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Abstract
Let K / Q_p be a finite Galois extension and D a (phi,Gamma)module over the Robba ring B and N_dR(D) its associated padic differential equation.
In the first part we give a generalization of the BlochKato exponential map for D using continuous Galoiscohomology groups H^i(G_K, W(D)) for the Bpair W(D) associated to D. We construct a big exponential map Omega_D,h for cyclotomic extensions of K for D in the style of PerrinRiou extending techniques of Berger, which interpolates the generalized BlochKato exponential maps on the finite levels.
In the second part we extend two definitions for pairings on D and its dual D^*(1) (resp. on N_dR(D) and its dual N_dR(D^*(1))) and prove a generalization of the reciprocity law, which relates these pairings under the big exponential map.
Finally, we give some results on the determinant associated to Omega_D,h, and formulate an integral version of a determinant conjecture in the semistable case. Further, we define iSelmer groups and show under certain hypothesis a torsion property.
Item Type:  Dissertation 

Supervisor:  Venjakob, Prof. Dr. Otmar 
Date of thesis defense:  30 April 2013 
Date Deposited:  16 May 2013 05:24 
Date:  2013 
Faculties / Institutes:  The Faculty of Mathematics and Computer Science > Department of Mathematics 
Subjects:  510 Mathematics 