bio | website | math.harvard.edu/~amathew |
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location | Cambridge, MA | |
age | ||
visits | member for | 5 years, 10 months |
seen | 11 hours ago | |
stats | profile views | 20,738 |
PhD student at Harvard.
Jul
23 |
comment |
Milnor descent for ring spectra
If you are looking for the case (which I think is relevant for "Milnor descent") of a derived version of a pushout along closed immersions, there is a positive result with connectivity hypotheses in Theorem 7.2 of DAG IX, as well as a counterexample if these are omitted (Warning 7.3). As I think is implicit in your post, the functor $F$ is automatically fully faithful, so the question is equivalent to essential surjectivity of $F$ (or conservativity of $R$). |
Jul
7 |
comment |
Intersections of ideals and nilpotence
@user26857: The former. I've edited to clarify this point. |
Jul
7 |
revised |
Intersections of ideals and nilpotence
added 19 characters in body |
Jul
7 |
asked | Intersections of ideals and nilpotence |
Jun
24 |
awarded | Favorite Question |
May
28 |
awarded | Nice Question |
May
24 |
awarded | Revival |
May
24 |
awarded | Nice Question |
May
23 |
answered | Compact objects in undercategories and filtered colimits |
Apr
26 |
awarded | Nice Answer |
Apr
8 |
awarded | Nice Question |
Mar
16 |
asked | Decomposition of symmetric powers of reduced regular representation modulo $p$ |
Mar
15 |
awarded | Good Answer |
Mar
6 |
comment |
Explict form of $E_\infty$-morphisms between differential graded commutative algebras
So, homotopy classes of $A_\infty$-maps $A \to B$ require in addition choosing a nullhomotopy (which is a torsor over $\pi_1 B$ in this case). |
Mar
6 |
comment |
Explict form of $E_\infty$-morphisms between differential graded commutative algebras
It is not true that the inclusion of $E_\infty$-algebras into $A_\infty$-algebras is fully faithful in characteristic zero. As an example, let $A$ be the (discrete) $E_\infty$-algebra $\mathbb{Q}[x,y]$ and let $B$ be an $E_\infty$-algebra with nontrivial $\pi_1$. As an $E_\infty$-algebra, $A$ is free on two generators, so homotopy classes of maps $A \to B$ give $\pi_0 B \oplus \pi_0 B$. As an $A_\infty$-algebra, $A$ is free on two generators $x,y$ together with a homotopy $xy \simeq yx$... |
Feb
19 |
awarded | Revival |
Feb
18 |
awarded | Nice Question |
Feb
12 |
awarded | Nice Question |
Feb
11 |
comment |
Lifting DG-categories to characteristic zero
@TylerLawson: I should clarify that I am interested in the stable case (so in your example, that would correspond to lifting modulo Morita equivalence). I am also interested in the question you raise, but I suspect there are counterexamples in the discrete case. |
Feb
11 |
asked | Lifting DG-categories to characteristic zero |