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14h
comment How transversality condition implies that a value is regular?
Looking over the whole question, perhaps the notation $T_pf$ for what I have written as $df_p$ is just what your textbook uses (but I have never seen this before)...
14h
comment How transversality condition implies that a value is regular?
+1 by the way, I love this kind of careful self-learning question.
14h
comment How transversality condition implies that a value is regular?
In your definition of transverse, I think you mean $T_{f(p)}N = T_{f(p)}S + df_p(T_pM)$?
17h
comment Local vs. global in the definition of a sheaf
@AnnaCarlaRusso - another example of two different sheaves with the same stalks is the example of vector bundles / invertible sheaves on a scheme mentioned in the OP. Any two have the same stalks, in fact, they have the same stalks as the structure sheaf. So, for example, over projective space, $\mathcal{O}(1)$ and the structure sheaf are distinct sheaves with the same stalks.
17h
accepted Local vs. global in the definition of a sheaf
Apr
26
comment Conceptual reason why a quadratic field has $-1$ as a norm if and only if it is a subfield of a $\mathbb{Z}/4$ extension?
+1 Thank you so much! I've read this over and look forward to the opportunity to properly work through the details. In the meantime, a clarification question: in the isomorphism $H^2(G,A) \cong A^G/N(A)$ you described (in case $G$ is cyclic and $A$ is abelian), the "norm map attached to $G$" means $A\rightarrow A$ given by $a\mapsto\prod_{g\in G} ga$, right?
Apr
26
comment Conceptual reason why a quadratic field has $-1$ as a norm if and only if it is a subfield of a $\mathbb{Z}/4$ extension?
+1 can you point me to any specific citations from the Jahresberichte (and are any in English translation)?
Apr
4
awarded  Nice Question
Apr
4
accepted Two points of view on constructible sets
Mar
27
comment Can the quotient by a nonabelian group yield an abelian singularity?
I asked a refinement of the question on MO, here: mathoverflow.net/questions/234558/… Jason Starr's first comment seems to provide an example.
Mar
26
revised Can the quotient by a nonabelian group yield an abelian singularity?
added 193 characters in body
Mar
26
comment Proofs of the form $(P\lor\neg P)\implies Q$
@AsafKaragila - I don't have any background in logic or model theory so I am way out of my element here but doesn't what you just asserted imply that a proof that RH is independent of ZFC would constitute a proof of RH? (If yes, it even seemed like you are saying you can replace ZFC with PA in that statement??)
Mar
26
comment Can the quotient by a nonabelian group yield an abelian singularity?
I have had an email exchange with Satriano leading to the conclusion that $\mathbb{P}(V)/A_5$ is indeed smooth, but in any case your answer has led me to realize that I asked slightly the wrong question.
Mar
26
awarded  Socratic
Mar
25
asked Two points of view on constructible sets
Mar
25
comment Prov that function is eventually periodic to origin.
@Nadia - I agree with Ethan Bolker. It can't actually always be zero after 6 iterations.
Mar
23
comment Prov that function is eventually periodic to origin.
It won't always just take 5 iterations! (If it did, then $n=5$ would have $f^n(x,y,z,w)=(0,0,0,0)$ for all $(x,y,z,w)\in\mathbb{Z}^4$.)
Mar
21
comment A non-singular quotient of $\mathbb{A}^n$ by a cyclic group is isomorphic to $\mathbb{A}^n$
@Dorebell - I think it's that the invariant algebra, because it is graded, is geomerically a cone, so it has a singular point at the origin unless it is actually affine space. I recently convinced myself of this so I would be happy to give you an argument if you'd like - let me know.
Mar
21
comment Contraction of an ideal
$(X,X^2-2)$ simplifies to $(X,2)$ because if an ideal contains $X$ then it must contain $X^2$, so if it also contains $X^2-2$ then it also contains $X^2 - (X^2 - 2) = 2$. Thus $(X,X^2-2)$ contains $(X,2)$. But also, $(X,2)$ contains $(X,X^2-2)$ because if an ideal contains $X$ and $2$ then it contains $X(X) - 2 = X^2 - 2$.
Mar
20
comment Can the quotient by a nonabelian group yield an abelian singularity?
+1 This reference is extremely useful to me. I am not sure if it answers my question, partly because I think based on my own calculations that the variety $\mathbb{P}(V)/A_5$ is smooth! (I am going to reach out to Satriano with the hope of getting clarity on this point.) More fundamentally because Satriano and Geraschenko are considering the projective action so it doesn't pick up the singularity at the origin of $V/A_5$. But in any case it is tremendously useful - thank you!