bio | website | wwwmath.uni-muenster.de/u/… |
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location | Münster, Germany | |
age | 27 | |
visits | member for | 4 years, 9 months |
seen | 57 mins ago | |
stats | profile views | 33,895 |
I am interested in the interactions between algebraic geometry and category theory. More specifically, I "model" algebraic geometry on cocomplete symmetric monoidal categories.
Here is a link to my PhD thesis. Comments are welcome.
Email: [my last name] [at] uni-muenster.de
Sep 15 |
awarded | Popular Question |
Sep 13 |
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When does sheaf cohomology commute with arbitrary direct sums?
Direct sums are filtered colimits of finite direct sums. And finite direct sums are no problem. |
Sep 10 |
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Canonical presentation of pro-modules over pro-rings
The maps $M_{j+1} \to M_i$ are surjective. It follows easily that each projection $\widehat{M} \to M_j$ is surjective (construct inverse images recursively). Hence, also $\alpha_j$ is surjective. |
Sep 10 |
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Canonical presentation of pro-modules over pro-rings
From $K_{ji} = M_{j+i} I_{ij}$ for all $i$ we only get $\widehat{K_j} = \varprojlim_i \, (M_{j+i} \cdot I_{ji})$, but why does this equal $\varprojlim_i \, M_{j+i} \cdot \varprojlim_i \, I_{ji} = \widehat{M} \widehat{I_j}$? Again, $\subseteq$ is unclear. |
Sep 10 |
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Canonical presentation of pro-modules over pro-rings
Thank you. But $\widehat{K_j} = \widehat{I_j} \widehat{M}$ is unclear to me (and clearly this is a direct reformulation of the claim). How do you prove $\subseteq$? |
Sep 8 |
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Canonical presentation of pro-modules over pro-rings
Sure, the isomorphisms belong to the data. A morphism $M \to N$ is a family of morphisms $M_i \to N_i$ compatible with the isomorphisms. Actually all this follows from the definition $\mathcal{M} := \varprojlim_i \, \mathsf{Mod}(A_i)$. |
Sep 8 |
asked | Canonical presentation of pro-modules over pro-rings |
Aug 30 |
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A short proof for $\dim(R[T])=\dim(R)+1$
R. Gilmer is the author, but of which paper? |
Aug 17 |
awarded | Popular Question |
Aug 14 |
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Coherent sheaves and Mitchell's embedding theorem
Some comments. a) The embedding theorem doesn't work (a priori) for all abelian categories - we need essentially small abelian categories. I suggest to look at the category of quasi-coherent sheaves of finite type (resp. of finite presentation) since that is essentially small. b) "coherent" is something stronger than "finitely generated" (although Hartshorne's book suggests this). c) Even for $\mathbb{P}^1_k$ the question is not easy to answer, I think, even though one understands the quasi-coherent sheaves very well here. |
Aug 14 |
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Pursuing an abelian categorical proof of the Zassenhaus Lemma
You may use the embedding theorem. The reason is that the embedding is fully faithful and exact. So it preserves intersections and sums of subobjects, and it reflects isomorphisms (basically everything you need). |
Aug 14 |
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symmetric monoidal dagger endofunctor categories
@DavidWhite: Day convolution needs colimits with distribute over the tensor product. |
Aug 14 |
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Existence of Colimits in the Definition of Locally Presentable Categories
@ZhenLin: What about making this an answer? |
Aug 4 |
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A short proof for $\dim(R[T])=\dim(R)+1$
@NeilStrickland: The following example can be found in Hutchins, Examples of Commutative Rings, Example 27: Let $k$ be a field and let $R = k(y)[[x]] \times_{k(y)} k$ the ring of those power series in $x$ with coefficients in $k(y)$ resp. $k$ for the constant term. Then $\dim(R)=1$ and $\dim(R[T])=3$. I've also read that actually every number between $\dim(R)+1$ and $2 \dim(R)+1$ may appear as $\dim(R[T])$. |
Jul 26 |
asked | Open covering of the Hilbert functor of points |
Jul 23 |
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Infinite Tensor Products
@ashpool: $U=K^x$, which is trivial when $K=\mathbb{F}_2$. |
Jul 21 |
awarded | Enlightened |
Jul 21 |
awarded | Nice Answer |
Jul 17 |
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Tensor product of pullbacks of abelian categories
Sorry but this doesn't help me. I doubt that universal properties will help (we interchange colimits with limits). Also it's unclear to me what is nice here. The transfinite recursion in the reflection is horrible. |
Jul 8 |
asked | Tensor product of pullbacks of abelian categories |