L Functions associated to galois representations
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We review how to construct an L-function from a representation \(\rho\colon Gal(\bar{K}/K) \to GL(V)\)
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We review how to construct an L-function from a representation \(\rho\colon Gal(\bar{K}/K) \to GL(V)\)
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I will attempt to explain what I am currently working on at varying levels of detail.
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I am writing down the basic theory of smoothness to have an easy refrence. This will mostly just be a summary of vakil chapter 13, but mostly just the results.
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We start with a reductive group \(G\) over some number field \(K\) with automorphic representation \(\pi\) of \(G(\mathbb{A}_F)\).
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Here’s a fact I didn’t believe when I first read it. The category of rings is complete.