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• Tags:
  • #todo/untagged
• Refs:
  • Harvard notes https://people.math.harvard.edu/~smarks/mod-forms-tutorial/mf-notes/galois-reps.pdf #resources/notes
• Links:
  • Artin L function

Galois representations

A possible conceptual explanation for the importance of Galois representations delivers the Tannaka-Krein theorem. Roughly, this states that knowing the representation theory is equivalent to knowing the group. The group you want to understand is the absolute Galois groups (with a profinite topology) via its Galois representations, and understand the Galois representation via automorphic forms. Perhaps one famous example is the Taniyama Shimura conjecture and consequently Fermat’s last theorem: A certain construction with the elliptic curve gave a Galois representation, and the later was then shown to correspond to an automorphic form.

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Semistable/admissible

See semistable and admissible representation,cyclotomic character, crystalline

Unramified