ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: Gajda, Wojciech, Faculty of Mathematics and Computer Sciences, The Adam Mickiewicz University Poznan, Poland On Galois cohomology of some p-adic representations Let F be a number field, p an odd prime, S a finite set of primes of F containing primes over p. Let G_{S} denote Galois group of the maximal Sramified extension of F. In the talk I am going to show that the p-torsion part of the group H^{2}(G_{S}, T), for p-adic representations

ρ : G_{S} − − − − > GL(T)

which come from CM elliptic curves and Jacobians of some Fermat curves, is generated by special elements of Deligne-Soule type cf. [BGK]. According to the weak Leopoldt conjecture Galois cohomology group H^{2}(G_{S}, T) for T ’s as above should be finite. I will also discuss the subgroup of infinitely divisible elements in the group H^{2}(G(F̄/F, T), where T is twisted Tate module of the Jacobian of a proper smooth curve over F. Methods of proofs come from algebraic K-theory.

[BGK] G. Banaszak, W. Gajda and P. Krason: “On Galois cohomology of some p-adic representations and etale K-theory of curves”, MPI preprint (1998), pp. 22.