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Results tagged with automorphic-forms
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An automorphic form is a well-behaved function from a topological group $G$ to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup $\Gamma \subset G$ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.
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Overview of automorphic representations for $SL(2)/{\mathbf{Q}}$?
In short: what does Labesse-Langlands say?
Slightly more precise: what are the cuspidal automorphic representations of $SL_2(\mathbf{A}_{\mathbf{Q}})$, together with multiplicities? Let's say that I …
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44
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Are there motives which do not, or should not, show up in the cohomology of any Shimura vari...
Let $F$ be a real quadratic field and let $E/F$ be an elliptic curve with conductor 1 (i.e. with good reduction everywhere; these things can and do exist) (perhaps also I should assume E has no CM, ev …
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Why isn't meromorphic continuation enough for converse theorems?
This is a very naive question which really does little more than highlight my ignorance of how converse theorems really work.
Take an algebraic gadget which should be conjecturally associated to an a …
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How badly can strong multiplicity one fail in the theory of automorphic representations?
Let $G$ be a connected reductive group over a global field $k$, and let $\pi=\otimes_w\pi_w$ and $\pi'=\otimes_w\pi'_w$ be two automorphic representations for $G$, where here of course $w$ is ranging …
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Constructing coherent sheaves on Shimura varieties.
Let me first run through the setting of my question in an example I understand well; that of modular curves. If $Y_1(N)$ denotes the usual modular curve over the complexes, the quotient of the upper h …
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11
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Simple explicit example of local Jacquet-Langlands theorem for inner forms of GL(n), and con...
This one will be very easy for the experts.
Let $F$ be a nonarch local field, let $n\geq1$ be an integer, choose $0\leq d<n$ and let $D$ be the central simple algebra over $F$ with invariant $d/n$ in …
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What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$...
Let me stress that I am only interested in $p$-adic fields in this question, for reasons that will become clear later. Let me also stress that in some sense I am basically assuming that the reader kno …
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