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Let $X$ be an algebraic variety (separated quasi-compact scheme of finite type) over a field $k$. One of the possible definitions of an ample line bundle goes as follows: Def 1: A line bundle $\ …

The theory of differential graded algebras (in char 0) and their modules has numerous applications in rational homotopy theory as well as algebraic geometry. I'm looking for a reasonably complete ref …

Let $SpecA=X$ be an affine noetherian scheme. Let $QCoh(X)$ denote the derived (stable $\infty$-)category of quasi-coherent sheaves on $X$. There are the following special full subcategories spanned b …

What are some interesting examples of accessible $\infty$-categories which are not presentable and not small? By interesting I mean a category which comes up naturally in a certain context and …

Let $A$ be non-positively graded commutative DG-algebra almost of finite type over a field $k$ of characteristic $0$. Most of these assumptions (affine, commutative, characteristic, bound) are only to …

Let $X$ be a smooth affine variety over $\mathbb{C}$ and let $\mathcal{D}_X$ be its algebra of differential operators. Consider $\mathcal{C}=\mathcal{D}_X$-$\text{mod}$, the stable $\infty$ category …

I'll be using homological grading throughout this question. Let $G$ be a compact connected lie group. The following isomorphisms are classical and can be proven using several methods: $$H^{\bullet}( …