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The sum of same powers of all matrices modulo p
Accepted answer
14 votes

[corrections applied, per Ilya and Anton] Consider the formal series $$ f(x) = \sum_{k=0}^\infty (\sum_A A^k) x^k $$ where $A$ runs through $p \times p$ matrices. It is equal to $\sum_A (I - Ax)^{-1}...

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Does Ind-completion commute with finite limits?
9 votes

Let $D$ be the derived category of k-vector spaces, and let $C$ be the part consisting of bounded chain complexes of finite-dimensional vector spaces. $D = \mathit{Ind}(C)$. Let $P$ be a finite ...

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How many Lagrangian submanifolds?
4 votes

There's an idea of Hitchin's that (all Lagrangian submanifolds)/(Hamiltonian isotopy) should be, at least approximately, the same as (all "special" Lagrangian submanifolds). "Special" is defined with ...

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is the category of coherent sheaves some kind of abelian envelope of the category of vector bundles?
2 votes

Mimicking the theory of projective resolutions, try this: Start with the category whose objects are pairs $(V_1,V_0,d:V_1 \to V_0)$ where the $V_i$ are vector bundles, and whose morphisms are pairs $(...

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