10
votes
Accepted
The relation between t-structures and derived category
Assume $\mathcal D$ is a presentable stable $\infty$-category with a $\mathrm t$-structure (which is accessible and compatible with filtered colimits), and let $\mathcal A$ be its heart, $\mathcal{D(A)...
- 15.8k
7
votes
Heart of a bounded $t$-structure on the derived category of coherent sheaves
One can construct t-structures on the bounded derived category of coherent sheaves on a smooth projective curve (or higher-dimensional variety) by tilting, see Bayer's notes, Prop. 3.6.1, and the ...
- 2,300
6
votes
Accepted
Chromatic t-structures?
To expand on Tim's answer, the arguments generalize to show that $Sp_{K(n)}$ admits no non-trivial t-structures in general.
The crucial ingredient is that $Sp_{K(n)}$ has no non-trivial localising or ...
- 2,197
6
votes
Chromatic t-structures?
The second question turns out to have a surprisingly easy negative answer. This is depressing on two counts: both that the answer is negative and that it's so easy.
Suppose that $Sp_{K(n)}$ has a $t$-...
6
votes
The relation between t-structures and derived category
I had reason to think about this a few years ago. When $\mathcal D$ arises as the derived category of an abelian category (with a possibly exotic $t$-structure), a construction of a realization ...
- 40.2k
5
votes
Accepted
On various relations between "additional axioms" for AB4 and Grothendieck abelian categories
I don't think (3) implies (1).
For example, the opposite category of the category of abelian groups satisfies (3), but is not AB5.
- 35.2k
4
votes
On various relations between "additional axioms" for AB4 and Grothendieck abelian categories
Obviously, (2) implies (1). Indeed, if directed colimits are preserved by a conservative exact functor taking values in a category where they are exact, then they are exact in the source category.
...
- 15.6k
2
votes
Monoidality of truncation of spectra
A number of statements equivalent to preservation of $E_n$-algebras under truncation are given in a paper I wrote with Michael Batanin called "Bousfield Localization and Eilenberg-Moore Categories". ...
- 30.3k
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