\(p\)-adic Representation Theory (PadicRep)

3.4 TODOs

Definition 75
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Define idempotented algebra.

Definition 76
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Uses

Define non-degenerated (also called unital) modules over an idempotented algebra.

Theorem 77
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Uses

Hecke algebra is an idempotented algebra.

Proof ▶
Definition 78
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Uses

Define the category of non-degenerated modules over the Hecke algebra.

Theorem 79 Main theorem
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Uses

The category of non-degenerated modules over the Hecke algebra of \(G\) is equivalent to the category of smooth \(\mathbb {C}\)-representations of \(G\).

Proof ▶