Title: Motivic cohomology, Milnor K-theory, and Galois cohomology
Abstract: This dissertation presents one of the possible foundations, based on motivic complexes, for the motivic cohomology of smooth varieties over a given base field .Its basic properties are discussed, as well as its relation to Milnor K-theory and to certain Galois cohomology groups of .In particular, we discuss the formulation in terms of motivic cohomology of the norm residue homomorphism, which compares the Milnor K-theory groups modulo a prime number different from the characteristic of with the Galois cohomology groups with coefficients in tensor powers of the module of -th roots of unity.Finally, we list some preliminary results used for characterizing the Bloch-Kato conjecture in terms of certain statements of motivic nature.