bio | website | math.berkeley.edu/~achinger |
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location | Berkeley | |
age | 28 | |
visits | member for | 5 years, 3 months |
seen | 5 hours ago | |
stats | profile views | 3,281 |
PhD student, UC Berkeley
May 1 |
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Action of automorphisms on cohomology with supports
Another comment: If $f:X\to X$ is an isomorphism, then $H^n_x(X, f^*(-))$ form a universal $\delta$-functor. The system of maps $f^* : H^n_x(X, -)\to H^n_x(X, f^*(-))$ forms a map between two universal $\delta$-functors, so it suffices to check whether $f^*:H^0_x(X, -)\to H^0_x(X, f^*(-))$ is an isomorphism. |
Apr 30 |
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Action of automorphisms on cohomology with supports
(An $f:X\to X$ induces maps $H^n_x(X, M)\to H^n_x(X, f^* M)$ and $H^n(X, f_* M)\to H^n(X, M)$ but there is no canonical way of identifying $f^* M$ and $f_* M$ with $M$...) |
Apr 30 |
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Action of automorphisms on cohomology with supports
How do automorphisms of $X$ act on $H^n_x(X, M)$? |
Apr 27 |
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Singularities of the moduli stack of polarized hyperkahler varieties
@abx that's right, but $H^2(X, \mathcal{O}_X)$ is nonzero for $X$ hyperkaehler, and we want to study deformations of a pair $(X, L)$. |
Apr 27 |
answered | Singularities of the moduli stack of polarized hyperkahler varieties |
Apr 27 |
revised |
Counterexamples to Elkik's theorem in the non-Noetherian case
corrected spelling of "Ramero" |
Apr 23 |
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A question about Weil restriction
In definition (1), $\pi_* \mathbb{G}$ is to be considered as a sheaf on the big Zariski (or etale, or ...) site of $C$, associating to a $C$-scheme $D$ the set ${\rm Hom}_{\tilde C}(D\times_C {\tilde C}, \mathcal{G})$, and then the definitions are equivalent. If we consider the small Zariski site of $C$, then of course the two definitions are not equivalent (often $\mathcal{G}$ will have no sections over Zariski opens). |
Apr 23 |
answered | Reflexive sheaves on stable curves |
Apr 22 |
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Deformation of vector bundle on projective space with same Hilbert polynomial as multiple of structure sheaf
This is probably not a very useful observation: if $E$ is stable, then a deformation of $E$ should be stable as well, hence cannot be trivial. Maybe for some obvious reasons I don't see, a v.b. with Hilbert polynomial the same as the trivial bundle cannot be stable... |
Apr 11 |
reviewed | Approve Intuition for Integral Transforms |
Apr 11 |
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Interpreting Frobenius pullback as an invariant differential in the case of an elliptic curve
Is $S$ affine? / Shouldn't $H^1(E, \mathcal{O}_E)$ be $R^1 f_* \mathcal{O}_E$? If $E=S$, we should have ${\rm Lie}(E/S)=0$... |
Mar 26 |
awarded | Self-Learner |
Mar 21 |
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Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian?
Brilliant! Thank you. |
Mar 21 |
accepted | Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian? |
Mar 17 |
revised |
Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian?
added 5 characters in body; edited title |
Mar 17 |
asked | Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian? |
Mar 13 |
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Covering of schemes and flatness
The normalization of a cuspidal curve is a bijective finite map which is not flat. |
Feb 19 |
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Artin approximation of a diagram
What do you mean by approximate? Whether there exists a $\phi'$ in some etale neighborhoods inducing $\phi$ upon completion? Then the answer is no as we can take $Z$ to be a point, $(X, x)=(\mathbb{A}^1, 0)$, $(Y, y) = (\mathbb{A}^1, 1)$ and $\phi = \exp$. Or approximate up to order $N$ for any given $N$? Then I think the answer is yes, because we can apply approximation to the graph of $\phi$. |
Feb 9 |
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Definition and sigularity of Ramified covers
In general the cyclic cover will be ramified everywhere on $D$, so if $D\cap {\rm Sing}(X)$ is big there is no hope. |
Feb 9 |
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Definition and sigularity of Ramified covers
Be careful, because the cyclic covers as defined need not be normal if $D$ is non-reduced: in the simple example $X=\mathbb{A}^1$, $D=2\cdot (x)$ the recipe gives the non-normal $\tilde X = {\rm Spec}(k[x,y]/(x^2-y^3)$. But it's easy to compute the normalization, which is ${\rm Spec_X} \bigoplus_{i=0}^{n-1} \mathcal{O}_X(\lfloor \frac{i}{n}D \rfloor)$. |