9 citations · 15 across the 6 of their papers we have counts for
12 papers
Generalized cohomology of pro-spectra
Daniel C. Isaksen
We present a closed model structure for the category of pro-spectra in which the weak equivalences are detected by stable homotopy pro-groups. With some bounded-below assumptions,…
Algebraic K-theory and sums-of-squares formulas
Daniel Dugger, Daniel C. Isaksen
We prove a result about the non-existence of certain sums-of-squares formulas over a field. This generalizes an old theorem which used topological K-theory to obtain obstruction co…
Completions of pro-spaces
Daniel C. Isaksen
For every ring R, we present a pair of model structures on the category of pro-spaces. In the first, the weak equivalences are detected by cohomology with coefficients in R. In the…
Flasque model structures for simplicial presheaves
Daniel C. Isaksen
By now it is well known that there are two useful (objectwise or local) families of model structures on presheaves: the injective and projective. In fact, there is at least one mor…
The Hopf condition for bilinear forms over arbitrary fields
Daniel Dugger, Daniel C. Isaksen
We settle an old question about the existence of certain "sums-of-squares" formulas over a field F (which are the simplest examples of composition formulas for quadratic forms). A…
Weak equivalences of simplicial presheaves
Daniel Dugger, Daniel C. Isaksen
The usual way of defining weak equivalences for simplicial presheaves is to require an isomorphism on all sheaves of homotopy groups. We unravel some of the machinery here, and giv…