Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 7108

(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.

5 votes
1 answer
466 views

Uses for (Framed) E2 algebras twisted by braided monoidal structure

$\newcommand{\C}{\mathcal{C}}$ $\newcommand{\g}{\mathfrak{g}}$ If $\C$ is a monoidal category (not necessarily a symmetric monoidal category), it's possible to define the notion of an algebra object $ …
Dmitry Vaintrob's user avatar
2 votes
0 answers
212 views

Do dg schemes have derived points?

Working over a base field $k$ of characteristic $0$, say $K$ is a field (over $k$) and $X$ is a ("nice" if necessary) dg scheme in the sense of Toen-Vezzosi and others, and say $X^0$ is the reduced lo …
Dmitry Vaintrob's user avatar
3 votes
Accepted

Perfect DG modules

Well by definition a DG module $X$ is perfect iff it is a direct summand of a module which is a finite iterated extension of free modules (it's then a nontrivial result that this property is the same …
Dmitry Vaintrob's user avatar
2 votes
1 answer
166 views

Variant of co-Tor in a bimodule category

Say $\mathcal{C}$ is a strict monoidal abelian category and $A$ is a coalgebra object in $\mathcal{C}$, with left co-modules $M$ and right co-module $N$ (also in $\mathcal{C}$). Then we have a notion …
Dmitry Vaintrob's user avatar
10 votes
2 answers
1k views

periodic cyclic homology and tilting in the sense of Scholze

Suppose $R$ is a perfectoid ring in mixed characteristic, and $R'$ its characteristic-$p$ tilt. Scholze's results on tilting say that the étale theories over $R$ and $R'$ are equivalent in an almost s …
Dmitry Vaintrob's user avatar
2 votes
1 answer
369 views

Nomenclature question: a morita-invariant way to say finite-dimensional?

Say $\mathcal{C}$ is the Abelian category of finitely-generated modules over some $k$-algebra $A$. Then an object $M\in \mathcal{C}$ is finite-dimensional over $k$ if and only if $\text{Hom}(P, M)$ is …
Dmitry Vaintrob's user avatar
47 votes
1 answer
3k views

A three-line proof of global class field theory?

There is an idea (I think originally due to Tate) that class field theory is fundamentally a consequence of Pontrjagin duality and Hilbert Theorem 90. I'm curious whether this can phrased using modern …
Dmitry Vaintrob's user avatar
8 votes
2 answers
1k views

Is there a finitely presented group with infinite homology over $\mathbb{Q}$?

Suppose $G$ is a discrete group given by finitely many generators with finitely many relations. Can the homology groups $H_i(G, \mathbb{Q})$, or equivalently $H_i(BG, \mathbb{Q})$ (topological homolog …
Dmitry Vaintrob's user avatar
2 votes

How much of a variety can be reconstructed from codimension-zero data?

I realized the answer is almost certainly "no", so I asked a better version of this question at How much of a variety can be reconstructed from codimension-zero data?. I think that if you take two hy …
Dmitry Vaintrob's user avatar
14 votes
1 answer
796 views

How much of a variety can be reconstructed from codimension-zero data?

This is an improved version of this question. Maybe it should be an edit -- I'm not sure what the MO convention is. I'm curious, more or less, how much information one can get out of the derived cate …
Dmitry Vaintrob's user avatar
1 vote
1 answer
330 views

How much of a variety can be reconstructed from codimension-zero data?

Suppose $X$ is a nice (finite type over $\mathbb{C}$, smooth and proper if necessary) variety. Suppose we're given the $\mathbb{C}$-points of $X$ as a set and for any finite subset $S\subset X$ we kno …
Dmitry Vaintrob's user avatar