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5h
comment Is there a consistent arithmetically definable extension of PA that proves its own consistency?
What about your first three conditions but we demand that PA prove that PA is contained in T?
5h
comment Counting isomorphism classes in open subsets of Bun_G
Yes, this is precisely what I need. I'm going to go through the argument to make sure it's fine in characteristic $p$...
1d
comment Counting isomorphism classes in open subsets of Bun_G
@TomDeMedts It is indeed.
1d
revised Counting isomorphism classes in open subsets of Bun_G
added 7 characters in body
2d
comment extending local systems on a neighbourhood
this is a really interesting question! I think the answer should be no in the case where $Y$ is an elliptic surface minus a section and $S$ is one of the fibers, but I didn't figure out how to prove it.
Feb
10
comment splitting property of etale covering
stacks.math.columbia.edu/tag/04GG part 7 or 8 is the statement you want. Etale morphisms to henselian local rings have sections, and connected etale with section implies isomorphism.
Feb
10
answered Lefschetz on étale fundamental group for quasi-projective varieties
Feb
10
asked Counting isomorphism classes in open subsets of Bun_G
Feb
6
comment Is there a finite test for isomorphisms of rigid monoidal abelian categories?
mathoverflow.net/questions/230380/…
Feb
6
comment Is there a finite test for isomorphisms of rigid monoidal abelian categories, part II
@TheoJohnson-Freyd Yes, there need not be any such symmetry (as far as I know), but if it exists then it is unique.
Feb
6
comment Is there a finite test for isomorphisms of rigid monoidal abelian categories?
I have accepted your answer and asked a new, different question, without the functor $F'$.
Feb
6
asked Is there a finite test for isomorphisms of rigid monoidal abelian categories, part II
Feb
6
accepted Is there a finite test for isomorphisms of rigid monoidal abelian categories?
Feb
6
comment Is there a finite test for isomorphisms of rigid monoidal abelian categories?
Good point. But I think the conditions for it to work are pretty mild. And anyways it's still true that we haven't proved the map factors through the fiber functor.
Feb
5
comment Is there a finite test for isomorphisms of rigid monoidal abelian categories?
Yes, but that functor does not necessarily factor through some arbitrary other functor. For instance, I claim every monoidal abelian category containing a rigid object admits a functor from $Rep_{SL_2}$ sending the standard representation to that object. See my other question: mathoverflow.net/questions/188090/non-abelian-freeness-of-su-2
Feb
5
comment Is there a finite test for isomorphisms of rigid monoidal abelian categories?
Thanks, that makes sense! I know how to do the group theory part, that's fine. Do you know what happens if I don't have a functor to Vect? Is there some counterexample you can construct?
Feb
5
awarded  Nice Question
Feb
3
asked Is there a finite test for isomorphisms of rigid monoidal abelian categories?
Feb
3
comment First Galois cohomology of Weil restriction of $\mathbb{G}_m$
It's important to note that Sasha asked for $\operatorname{Gal}(L/K)$-cohomology and not $\operatorname{Gal}(K)$ cohomology. In particular, this is the source of the assumption that $L/K$ be Galois! To check that your answer applies, we apply a spectral sequence to equation the $\operatorname{Gal}(K)$-cohomology of a group scheme to the $\operatorname{Gal}(L/K)$ cohomology of its $\operatorname{Gal}(L)$-cohomology, then observe that its $\operatorname{Gal}(L)$-cohomology is equal to its $L$-points in degree $0$ (obvious) and vanishes in higher degree (Hilbert 90).
Feb
1
comment Paths in $\mathrm{Spec} \, \mathbb{Z}$ and Kim's proof of Siegel's theorem for $\mathbb{P}^1 \setminus \{0,1,\infty\}$
@VesselinDimitrov I fail to see how $abc$ suggests anything along these lines, because all $abc$ bounds are in terms of the radical, not the number of prime factors.