Motivic cohomology and characterizations of the Bloch-Kato conjecture
Galois Theory, profinite groups and applications in quadratic forms
Partial actions, Galois cohomology and seven term exact sequences
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Motivic cohomology, Milnor K-theory, and Galois cohomology
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| Author(s): |
Daniel de Almeida Souza
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2022-03-24 |
| Examining board members: |
Hugo Luiz Mariano;
Oliver Lorscheid;
Hugo Rafael de Oliveira Ribeiro
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| Advisor: | Hugo Luiz Mariano |
| 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 $k$. Its basic properties are discussed, as well as its relation to Milnor K-theory and to certain Galois cohomology groups of $k$. 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 $l$ different from the characteristic of $k$ with the Galois cohomology groups with coefficients in tensor powers of the module of $l$-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. (AU) | |
| FAPESP's process: | 19/09534-4 - Motivic cohomology and characterizations of the Bloch-Kato conjecture |
| Grantee: | Daniel de Almeida Souza |
| Support Opportunities: | Scholarships in Brazil - Master |