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Thomas Poguntke's user avatar
Thomas Poguntke
  • Member for 9 years, 9 months
  • Last seen more than 6 years ago
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 Yearling
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Characters of the kernel of the norm map of an extension of local fields
Doesn’t the short exact sequence $1 \to \widehat{F^{\times}} / \widehat G \to \widehat{E^{\times}} \to \widehat K \to 1$ imply that any character of $K$ has infinitely many extensions to $E^{\times}$?
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About enveloping algebras of direct sums
If by one-to-one you mean isomorphism, then yes; the Yoneda lemma holds for any category, including $\mathcal C$.
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About enveloping algebras of direct sums
This is the Yoneda lemma: if $\alpha^*$ is a bijective for all $A \in \mathcal C$, then $\alpha$ is an isomorphism in $\mathcal C$.
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About enveloping algebras of direct sums
I've specified the categories, and I hope this makes it clearer.
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About enveloping algebras of direct sums
added 251 characters in body
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About enveloping algebras of direct sums
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About enveloping algebras of direct sums
Yes, that is what I meant (just on the other side of the Yoneda embedding).
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About enveloping algebras of direct sums
Ah, sorry, I thought $\alpha$ was supposed to be an isomorphism of algebras, which only makes sense if $\mathfrak g_1$ and $\mathfrak g_2$ commute.
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About enveloping algebras of direct sums
If you apply $\text{Hom}(-,A)$ to your map for an $R$-algebra $A$, won't both sides be described by $(f,g) \in \text{Hom}(\mathfrak g_1,A) \times \text{Hom}(\mathfrak g_2,A)$ such that $[f(x),g(y)] = 0$ for all $x,y$?
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 Vox Populi
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Double-categorical refinement of twisted arrow category: does it have a name?
As a bisimplicial set, it is also called the total décalage of (the nerve of) $C$.
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 Suffrage
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Is quotient by maximal destabilizing sheaf, torsion-free?
I don't think there is such a thing as geometrically (non-)torsion-free.
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 Commentator
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Notation for the automorphisms of a $S$-scheme over automorphisms of $S$
$\operatorname{Aut}(s)$?
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How do morphism of Groups be the same as the Group-Representation
This follows from Tannaka's reconstruction theorem (cf. math.stackexchange.com/q/996422), at least if $k$ is commutative.
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The symmetric product of a stack and its motive
This paper seems to elaborate a bit on what Ekedahl does. arxiv.org/abs/1008.5063
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The non-existence of the fine moduli scheme of vector bundles. Why?
More precisely, $\mathcal E$ is a vector bundle on $C \times_k M$, namely corresponding to the identity morphism $\phi = \text{id}\!: M \to M$.
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The $\mathrm{Hom}(E_2,E_1)$-action on $\mathrm{Ext}^1(E_2,E_1)$
See here: mathoverflow.net/questions/223996/…
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