Abstract: One way to study the structure of a field is to equip it with an absolute value. Roughly, an absolute value, sometimes called a valuation, gives a measurement of size for elements. Furthermore, it induces a topological field structure and unlocks to us analytic tools. In this talk, we give a brief introduction to the theory of absolute values. In particular, we will look at some cases in which absolute values can be classified, up to their induced topologies. We will also see how absolute values can be extended to larger fields.
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