# Tagged Questions

Questions about tilting theory, including questions on tilting modules, tilting sheaves, tilting complexes, and tilting objects.

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### Socle of tilting modules in the BGG category $\mathcal{O}$ over a semisimple Lie algebra

Suppose that $\mathfrak{g}$ is a finite dimensional, complex, semisimple Lie algebra. Let $\mathcal{O}$ be the BGG category over $\mathfrak{g}$. Tilting module theory play an important role in the ...
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### Tilting modules in positive characteristic

Consider the category of finite-dimensional representations for the algebraic group $\mathrm{SL}(n)$ in characteristic $p$. I know very little about this but am told there is a highest weight category ...
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### Could Partial Tiltings be studied as Almost Complete Tiltings?

The first part of what follows is a brief recap of the definitions, setting and motivations for my questions. Experts can find the questions at the end. Here $k$ denotes an algebraically closed field,...
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### An equivalence of derived categories by Happel-Reiten-Smalø

I have a problem in understanding the proof of a theorem by Happel-Reiten-Smalø. The original reference is this article http://arxiv.org/abs/0911.4473 . I write down the text of the theorem and a ...
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### 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 $B$ ...
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### A canonical algebra of type $(2,2,r)$ is derived equivalent to a path algebra of type $\tilde{D}_{r+2}$ (references)

According to several articles I could find, a canonical algebra of type $(2,2,r)$ is derived equivalent to a path algebra of type $\tilde{D}_{r+2}$, where $r \geq 2$. I don't know how to obtain this ...
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### Tensor product of sheaves and modules

Hello to all, I have been looking quite recently at the following theorem: Let $X$ be a projective variety and $T$ a tilting object for $X$. If $A:=End(T)$ is the associated endomorphism algebra, ...
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### 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 ...