Keenan Kidwell
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Registered User
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I'm a graduate student at UT Austin. My e-mail address is kkidwell@math.utexas.edu.
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1d |
accepted | Degree of a finite locally free group scheme over a base scheme of characteristic p |
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1d |
revised |
Degree of a finite locally free group scheme over a base scheme of characteristic p deleted 92 characters in body; deleted 15 characters in body |
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1d |
revised |
Degree of a finite locally free group scheme over a base scheme of characteristic p added 2 characters in body; added 233 characters in body; added 31 characters in body; deleted 148 characters in body |
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1d |
answered | Degree of a finite locally free group scheme over a base scheme of characteristic p |
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May 13 |
revised |
Stein manifolds definiton edited tags |
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May 6 |
comment |
Cuspidal automorphic representations as the space of $K$-finite vectors in a unitary cuspidal automorphic representation. Thank you Marc! This is very helpful. |
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May 4 |
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Cuspidal automorphic representations as the space of $K$-finite vectors in a unitary cuspidal automorphic representation. Dear @Marc, Could you possibly be more precise, or suggest a reference for the passage between the unitary point of view and the more algebraic point of view? I'm aware Flath's theorems on factorizability into restricted tensor products, but for example, I don't know why if I complete an automorphic representation and take the K-finite vectors (i.e. the algebraic direct sum of the $K$-isotypic components) I recover the representation with which I began. |
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May 4 |
revised |
Cuspidal automorphic representations as the space of $K$-finite vectors in a unitary cuspidal automorphic representation. edited title |
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May 4 |
asked | Cuspidal automorphic representations as the space of $K$-finite vectors in a unitary cuspidal automorphic representation. |
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May 1 |
comment |
Reason for studying coherent sheaves on complex manifolds. Well, Oka's coherence theorem says the structure sheaf of a complex manifold is coherent...that's interesting. |
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Apr 27 |
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Reference for Rationality in Algebraic Groups in the Language of Schemes? Have you looked at the notes from Brian Conrad's courses on linear algebraic groups? They are of course thoroughly modern. In particular, there are course notes covering the entirety of the first semester which might have some of what you want. |
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Apr 23 |
accepted | Finitely Generated Commutative Z-algebra. |
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Apr 23 |
comment |
Finitely Generated Commutative Z-algebra. Thanks @Zhen Lin. |
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Apr 23 |
answered | Finitely Generated Commutative Z-algebra. |
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Apr 21 |
comment |
Are there modular elliptic curves over a field extension of $\mathbb{Z}[i]$? Just to echo François Brunault's comment, the ``modularity theorem" over, e.g., a totally real field, doesn't refer to the existence of a covering by a modular curve, but by the equality of the Hasse-Weil $L$-function with the $L$-function of a Hilbert modular eigenform of parallel weight $2$. Under certain hypotheses on the elliptic curve, this implies the existence of a covering by a Shimura curve, analogous to a modular curve, but these hypotheses do not always hold (they fail for example when the curve has good reduction everywhere and the field has even degree). |
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Apr 9 |
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$k[[x]]$ as a $(k[[x]])^p$ module for ugly fields Dear @Fernando, $k^p$ means $\{\alpha^p:\alpha\in k\}$, i.e., the image of the Frobenius endomorphism of $k$. |
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Apr 9 |
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Finite Unipotent Groups: References I would guess that $U(n,\mathbf{F}_q)$ means upper triangular $n\times n$ matrices with $1$'s on the diagonal. |
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Apr 4 |
awarded | ● Citizen Patrol |
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Mar 22 |
revised |
How does one make sense of the $\mathbf{C}_p$-points of a rigid analytic space over $\mathbf{Q}_p$? deleted 1 characters in body |
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Mar 6 |
comment |
Open idempotents in modules over a local ring Dear @Martin, The ring of integers of $\mathbf{C}_p$, the completion of the algebraic closure of $\mathbf{Q}_p$, has this property, and in a valuation ring, finitely generated ideals are principal, so the proof is the same as for principal ideal domains, i.e., to prove that $M$ is flat, prove that $I\otimes M\rightarrow M$ is injective for all finitely generated ideals. |
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Mar 2 |
awarded | ● Yearling |
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Feb 21 |
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How does one make sense of the $\mathbf{C}_p$-points of a rigid analytic space over $\mathbf{Q}_p$? Dear @Qing, Thank you! This clears things up for me. |
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Feb 11 |
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Open subset in the flat topology on Spec(R) I'm not sure if it's true in the non-Noetherian case, but if $R$ is Noetherian, then a subset $S$ of $\mathrm{Spec}(R)$ is (Zariski) open if and only if it is constructible (in the sense of the Stacks Project) and stable under generalization. |
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Feb 8 |
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Reference for rigid analytic GAGA Have you looked at the papers\notes of Brian Conrad? |
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Jan 28 |
awarded | ● Civic Duty |
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Nov 25 |
revised |
How does one make sense of the $\mathbf{C}_p$-points of a rigid analytic space over $\mathbf{Q}_p$? I changed the title so that it reflected more accurately my actual question. |
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Nov 25 |
asked | How does one make sense of the $\mathbf{C}_p$-points of a rigid analytic space over $\mathbf{Q}_p$? |
