ya-tayr
  • Member for 9 years, 1 month
  • Last seen more than 6 years ago
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}...

View answer
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 ...

View answer
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 ...

View answer
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 $(...

View answer