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Watch a mathematics lecture from Kyoto University Research Institute for Mathematical Sciences' 42nd Public Mathematics Course, where Assistant Professor Hironaga Koshikawa explores the Frobenius map and its applications. Learn about the similarities between integers and polynomial rings, finite fields, and primitive roots. Discover how in algebras where prime p equals zero, the operation of raising numbers to the p-th power is called the Frobenius map, and understand its significance in controlling Galois theory of finite fields, leading to the Weil conjecture. Explore how the "lifting" of the Frobenius map has been historically considered in situations where p is not equal to zero, and examine its renewed importance in recent research. The lecture introduces finite fields and Witt vectors from an elementary perspective, featuring interactive Q&A sessions at the beginning and end of the presentation.
