Keerthi Madapusi Pera
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May 12 |
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Is there an algebraic curve over Q which is not modular? Nice. Thanks!... |
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May 12 |
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Is there an algebraic curve over Q which is not modular? Wouldn't you expect the modular forms to be attached to automorphic reps of GSpin? |
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May 5 |
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log étale topology What is your definition of log etale topology? |
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Apr 24 |
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Finite Flat Group Schemes for Modular Forms of Higher Weight What about the mod $\ell$ representation though? Isn't it Barsotti-Tate under weaker assumptions? |
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Apr 3 |
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Moduli Spaces of Higher Dimensional Complex Tori $SL$ should be $Sp$. |
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Mar 26 |
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Galois descent for semilinear endomorphisms Does $\sigma$ preserve $K$? |
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Mar 24 |
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Two different definitions of $\sigma$-L-spaces in Kottwitz I and II No, in this case the first definition would be stronger. I'd recommend looking at a basic reference, like Serre's Local Fields. |
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Mar 22 |
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Two different definitions of $\sigma$-L-spaces in Kottwitz I and II Sorry, didn't realize wccanard had already made essentially the same comment. |
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Mar 22 |
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Two different definitions of $\sigma$-L-spaces in Kottwitz I and II If $k$ is the algebraic closure of the residue field of $F$, then the completion of $F^{nr}$ is exactly the compositum of $F$ and the fraction field of $W(k)$. |
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Mar 15 |
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Definition of relative Picard functor pranavk--Don't you need $f$ to also be flat? |
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Mar 3 |
accepted | Status of Grothendieck’s conjecture on homomorphisms of abelian schemes |
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Mar 3 |
answered | Status of Grothendieck’s conjecture on homomorphisms of abelian schemes |
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Mar 1 |
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Status of Grothendieck’s conjecture on homomorphisms of abelian schemes More precisely, what my comment shows is that we have $Hom(A_{\eta},B_{\eta})=Hom(A,B)$. So, by Zarhin, $u_{\ell}$ arises from an element of $Hom(A,B)\otimes\mathbb{Z}_{\ell}$. To check that some multiple of it actually lies in $Hom(A,B)$, it suffices to check that, for some point $s\in S$, the image in $Hom(A_s,B_s)\otimes\mathbb{Z}_{\ell}$ lies in $Hom(A_s,B_s)$. |
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Mar 1 |
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Status of Grothendieck’s conjecture on homomorphisms of abelian schemes Ah, that's right! I was being cavalier as usual. I think the existence of $u_s$ should force it to actually lie in $Hom(A_{\eta},B_{\eta})$. |
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Mar 1 |
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Status of Grothendieck’s conjecture on homomorphisms of abelian schemes Suppose that $S$ is a normal variety over $\mathbb{F}_p$ with generic point $\eta\to S$. Then, by Zarhin, there exists a homomorphism of the generic fibers $u_{\eta}:A_{\eta}\to B_{\eta}$ giving rise to $u_{\ell}$ (one doesn't even need the existence of $u_s$ for this). Now, by Proposition 2.7 in Chai-Faltings 'Degeneration of abelian varieties', $u_{\eta}$ extends over all of $S$. The idea basically is to use the Neronian property of abelian schemes to show that the closure of the graph of $u_{\eta}$ in $A\times B$ maps isomorphically onto $A$. |
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Feb 27 |
awarded | ● Nice Answer |
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Feb 22 |
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Semicontinuity for complexes ulrich--That reference seems to answer the question as well as one could hope to. Maybe you should put it down as an answer? |
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Feb 21 |
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Semicontinuity for complexes I think with the $^L$ the perfectness is what you need (I wonder if it's actually necessary). Without the $^L$, you probably need to require that the cohomology of $F$ is flat over $Y$ (I'm guessing $F$ is bounded). |
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Feb 21 |
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Semicontinuity for complexes hmm...is that a contradiction if one is taking derived tensor products like the OP is doing? |
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Feb 21 |
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Semicontinuity for complexes ulrich--Is that because, locally on $Y$, every coherent sheaf admits a finite free resolution? Also, that reminds me that I should have added the adverb 'locally' in front of quasi-isomorphic. |
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Feb 21 |
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Semicontinuity for complexes Call the morphism $\pi$. I think you're good if $R\pi_*F$ is quasi-isomorphic to a perfect complex. This is true if $F$ is flat over $Y$, and as far as I can tell is the only non-trivial input in this case. |
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Feb 3 |
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global units on moduli spaces of abelian varieties If you allow yourself to invert all the primes whose squares divide $d$, $A_{g,d,1}$ (as a stack) admits a compactification (the so-called minimal or Baily-Borel-Satake compactification) with normal, geometric irreducible fibers, and whose boundary has codimension at least $2$. In particular, one does not expect to find any interesting units in this case. |
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Jan 31 |
accepted | On Weil’s characters of type (A) |
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Jan 31 |
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On Weil’s characters of type (A) Also, as Florian points out in the comments above, pretty much the same proof appears in Patrikis's thesis. |
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Jan 31 |
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On Weil’s characters of type (A) Edits made. I think the proof is now correct. |
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Jan 31 |
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On Weil’s characters of type (A) added 1498 characters in body; deleted 221 characters in body |
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Jan 31 |
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On Weil’s characters of type (A) Hi Hugo, you're right! I was confused about why I seemed to be getting post facto that $f_{\sigma\iota}+f_{\bar{\sigma}\iota}$ was independent also of $\sigma$. But of course I need to show this a priori! I'll see if I can fix the argument. |
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Jan 31 |
answered | On Weil’s characters of type (A) |
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Jan 30 |
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On Weil’s characters of type (A) Also, do you mean Dirichlet's theorem, rather than Minkowski's? |
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Jan 30 |
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On Weil’s characters of type (A) See Laurent Fargues's great article 'Motives and automorphic forms: the potentially abelian case', available here: www-irma.u-strasbg.fr/~fargues/Motifs_abeliens.pdf It's Proposition 1.12. |
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Jan 25 |
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Absorbing ramification and factoring finite flat maps You might want to look at Abhyankar's Lemma and its variations. See SGA 1, Exp. XIII, Appendice I, which says that if $Y$ is regular, and $\phi$ is tamely ramified, then you can remove the ramification via an appropriate base change of $Y$. There's also the Nagata-Zariski purity theorem (SGA 1, Exp. X, Theoreme 3.1), which says that, when $Y$ is regular and $X$ normal, then the locus in $Y$ where $\phi$ is ramified has to be of pure co-dimension $1$. |
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Jan 9 |
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Stein factorization and flatness @kreck: You're absolutely right. Thanks for the correction. |
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Jan 8 |
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Stein factorization and flatness This might or might not be helpful: If $Y$ is reduced, then the flatness of $f_*\mathcal{O}_X$ is equivalent to its formation being compatible with arbitrary base-change. |
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Jan 5 |
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Submodule of a Kisin module Moreover, they have to satisfy the condition that the cokernel of $\phi$ is killed by $u^e$ (that's the reduction of the Eisenstein; $e$ is the ramification index of $K$). |
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Jan 5 |
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Submodule of a Kisin module Are these sub-modules $\phi$-stable though? |
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Dec 31 |
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sign in the polarization of Hodge structures I've also been confused by this issue, but as for your question 1: the answer is that the natural pairing on primitive cohomology is a polarization up to $(-1)^{n(n+1)/2}$. This of course seems to disagree with your sign by a factor of $(-1)^n$! |
