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Milnor K-Invariants of Groups of Multiplicative Type

  • Author(s): Wertheim, Alexander Joseph
  • Advisor(s): Merkurjev, Alexander
  • et al.

Let $G$ be an algebraic group over a field $F$ of arbitrary characteristic. A type $i$-degree $n$ Milnor $K$-invariant of $G$ is an element of $Inv^{i}(G, K^{M}_{n} \otimes_{\mathbb{Z}} \mathbb{Q}/\mathbb{Z})$. This goal of this thesis is to compute the group of degree $n$ Milnor $K$-invariants for certain algebraic groups $G$ when $n = 1, 2$. The main results are divided among two chapters. In Chapter 2, we compute the type-one (homomorphic) degree one Milnor $K$-invariants for algebraic groups of multiplicative type. We also compute the type-zero (homomorphic) degree one Milnor $K$-invariants for reductive groups. In Chapter 3, we compute the type-one degree two Milnor $K$-invariants for algebraic tori; this is joint work with Alexander Merkurjev.

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