**5**

votes

**0**answers

206 views

### Not isomorphic varieties with isomorphic tilting algebras

Let $X$ be a smooth projective variety over a field, than tilting object $T$ on $X$ is a perfect complex that is a compact generator of the derived category $\operatorname{D}(QCoh(X))$ and satisfies ...

**4**

votes

**0**answers

173 views

### 2-periodic derived equivalence

Let $A$ and $B$ be finite-dimensional algebras with finite global dimension over some field (in fact I am thinking of rational incidence algebras of finite posets).
Suppose we know that $A$ and $B$ ...

**3**

votes

**0**answers

224 views

### Global dimension of endomorphism algebra of a coherent sheaf

Let $X$ be a smooth projective variety over algebraically closed field of characteristic zero. In one of the versions of definition of tilting object $\mathcal{F}$ on $X$ there is a requirement that ...

**3**

votes

**0**answers

421 views

### Geometric picture behind tilting sheaves

I am trying to read "Tilting exercises" and have trouble to see any geometric pictures behind the formulas.
So my questions are, how to think about tilting perverse sheaves?
Are they just formal ...

**0**

votes

**0**answers

161 views

### For a pair of non-commutative ring $(R, S)$, is there a faithfully semidualizing $(R, S)$-bimodule?

Given a pair of non-commutative rings $(R, S)$, how to construct a faithfully semidualizing $(R, S)$-bimodule?
Henrik Holm and Diana White introduced the concept of faithfully semidualizing ...