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  "body": "\n## Summary\n\nMilnor K-theory attaches to a field $K$ a sequence of abelian groups $K_n^M(K)$, see the [[definition|HEVWQ6B77W]].\nThey are generated by symbols $\\set{a_1, \\ldots, a_n}$ of nonzero elements.\nThe symbols are multilinear and satisfy the Steinberg relation $\\set{a, 1 - a} = 0$.\nIn degrees $0$, $1$ and $2$ it agrees with the algebraic K-theory groups $\\Z$, $K^\\times$ and $K_2(K)$.\nThe [[norm residue isomorphism theorem|5Q5VN56QH4]] identifies its reduction modulo $\\ell$ with [[Galois cohomology|9MPCZ3EAJM]].\nIt also connects with quadratic forms through the Milnor conjecture.\n\n## Explanations\n\n### L1 human\n\nStart with the nonzero elements of a field under multiplication.\nForm \"products\" of $n$ of them, written $\\set{a_1, \\ldots, a_n}$, which behave like products in each slot.\nAdd one extra rule: a symbol vanishes when two of its entries add up to $1$, as in $\\set{2, -1} = 0$ over $\\Q$.\nThe groups that result are simple to define, yet they carry deep arithmetic information about the field.\n",
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