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Dustin Clausen

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Name Dustin Clausen
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Jun
10
 awarded ● Nice Answer
May
29
 awarded ● Nice Answer
May
28
 accepted Explicit description of boundary map in algebraic K-theory
May
28
 revised Explicit description of boundary map in algebraic K-theory
added 87 characters in body
May
27
 awarded ● Necromancer
May
27
 awarded ● Self-Learner
May
27
 answered Explicit description of boundary map in algebraic K-theory
Apr
10
 awarded ● Enlightened
Apr
10
 awarded ● Nice Answer
Apr
10
 accepted Etale homology via étale cosheaves
Apr
4
 awarded ● Good Answer
Feb
14
 comment Etale homology via étale cosheaves
(for a nice reference from the Cech perspective, see Mitchell's paper math.uiuc.edu/K-theory/0346/topk.pdf in section 3.)
Feb
14
 comment Plus construction considerations.
Well, in general it's not deterministic, even if you know Steenrod actions on the homology. I had in mind whatever you can get in low degrees from considerations as in Goodwillie's answer. In our case that gives K_1 = H_1(GL(R)) and K_2 = H_2([GL(R),GL(R)]) and K_3 = H_3(universal central extension of [GL(R),GL(R)]), but there we stop because H_3 doesn't have as nice a group theory interpretation. Another fact (at least provided the H-space is actually a loop space) is that the rational homotopy maps isomorphically to the primitives of the Hopf algebra structure on the rational homology.
Feb
14
 comment Etale homology via étale cosheaves
No, I literally mean Pontryagin dual. Think of it this way: etale cohomology with Z/l^infty coefficients should be equal to continuous homomorphisms from \pi_1(X) to Z/l^infty, or to continuous homomorphisms from H_1(X;Z_l) to Z/l^infty. This just means that H^1(X;Z/l^infty) is Pontryagin dual to H_1(X;Z_l).
Feb
14
 answered Etale homology via étale cosheaves
Feb
10
 awarded ● Enlightened
Feb
10
 awarded ● Nice Answer
Feb
10
 awarded ● Yearling
Feb
9
 accepted Plus construction considerations.
Feb
9
 answered Plus construction considerations.
Jan
26
 comment Conceptual proofs for the computation of the structure sheaf
Just a comment: your first proof is an unwinding of the simple proof "apply faithfully flat descent to the map A --> \prod_{u\in U} A_u".