Daniel Dugger

The motivic Adams spectral sequence (2009)

Abstract. We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.

ENRICHED MODEL CATEGORIES AND AN APPLICATION TO ADDITIVE ENDOMORPHISM SPECTRA (2008)

We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field. We discuss several features of the associated Adams spectral sequence, including the basic...

4. Categories of k-invariants and Eilenberg-MacLane objects 9 (2008)

Abstract. We define the notion of an additive model category and prove that

Large annihilators in Cayley-Dickson algebras (2008)

Abstract. We give a functorial construction of k-invariants for ring spectra, and use these to classify extensions in the Postnikov tower of a ring spectrum. Contents

Daniel K. Biss, Daniel Dugger, C. Isaksen

Abstract. Cayley-Dickson algebras are non-associative R-algebras that generalize the well-known algebras R, C, H, and O. We study zero-divisors in these algebras. In particular, we show that the...

ENRICHED MODEL CATEGORIES AND AN APPLICATION TO ADDITIVE ENDOMORPHISM SPECTRA (2008)

ENRICHED MODEL CATEGORIES AND AN APPLICATION TO ADDITIVE ENDOMORPHISM SPECTRA (2008)

Abstract. We define the notion of an additive model category and prove that any

A curious example of two model categories and some associated differential graded algebras (2007)

Abstract. We define the notion of an additive model category and prove that any

A curious example of two model categories and some associated differential graded algebras (2007)

The paper gives a new proof that the model categories of stable modules for the rings Z/(p^2) and (Z/p)[\epsilon]/(\epsilon^2) are not Quillen equivalent. The proof uses homotopy endomorphism ring...

Large annihilators in Cayley-Dickson algebras II (2007)

"Vegeu el resum a l'inici del document del fitxer adjunt."

Biss, Daniel K., Christensen, J. Daniel, Dugger, Daniel, Isaksen, Daniel C.

We establish many previously unknown properties of zero-divisors in Cayley-Dickson algebras. The basic approach is to use a certain splitting that simplifies computations surprisingly.

The Hopf condition for bilinear forms over arbitrary fields (2007)

Dugger, Daniel, Isaksen, Danierl C.

Etale homotopy and sums-of-squares formulas (2006)

Classification spaces of maps in model categories (2006)

This paper uses a relative of BP-cohomology to prove a theorem in characteristic p algebra. Specifically, we obtain some new necessary conditions for the existence of sums-of-squares formulas over...

Topological equivalences for differential graded algebras (2006)

This paper corrects a small mistake in a paper of Dwyer-Kan, and uses this to identify homotopy function complexes in a model category with the nerves of certain categories of zig-zags.

Postnikov extensions of ring spectra (2006)

We investigate the relationship between differential graded algebras (dgas) and topological ring spectra. Every dga C gives rise to an Eilenberg-Mac Lane ring spectrum denoted HC. If HC and HD are...

Enriched model categories and an application to additive endomorphism spectra (2006)

We give a functorial construction of k-invariants for ring spectra, and use these to classify extensions in the Postnikov tower of a ring spectrum.

Spectral enrichments of model categories (2006)

We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian...

Topological equivalences for differential graded algebras (2006)

We prove that every stable, presentable model category can be enriched in a natural way over symmetric spectra. As a consequence of the general theory, every object in such a model category has an...

Large annihilators in Cayley-Dickson algebras (2005)

Abstract. We investigate the relationship between differential graded algebras (dgas) and topological ring spectra. Every dga C gives rise to an Eilenberg-Mac Lane ring spectrum denoted HC. If HC and...

Biss, Daniel K., Dugger, Daniel, Isaksen, Daniel C.

Cayley-Dickson algebras are an infinite sequence of non-associative algebras starting with the reals, complexes, quaternions, and octonions. We study the zero-divisors in the higher Cayley-Dickson...

Spectral enrichments of model categories (2005)

C.: Motivic cell structures (2005)

We prove that every stable, combinatorial model category has a natural enrichment by symmetric spectra (or more precisely, a natural equivalence class of enrichments). This in some sense generalizes...

Daniel Dugger, Daniel C. Isaksen

Abstract An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of...

Documenta Math. 357 Algebraic K-Theory and Sums-of-Squares Formulas (2005)

Daniel Dugger, Daniel C. Isaksen, Communicated Stefan Schwede

Abstract. We prove a result about the existence of certain ‘sums-ofsquares’ formulas over a field F. A classical theorem uses topological K-theory to show that if such a formula exists over R,...

K-theory and derived equivalences (2004)

Notes on the Milnor conjectures (2004)

We show that if two rings have equivalent derived categories, then they have the same algebraic K-theory. Similar results are given for G-theory and for a large class of abelian categories.

Algebraic K-theory and sums-of-squares formulas (2004)

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

DOI: 10.1007/s00209-003-0607-y Topological hypercovers and A 1-realizations (2004)

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 conditions when the...

Daniel Dugger, Daniel C. Isaksen

Abstract. We show that if U ∗ is a hypercover of a topological space X then the natural map hocolim U∗→X is a weak equivalence. This fact is used to construct topological realization functors...

Motivic cell structures (2003)

The Hopf condition for bilinear forms over arbitrary fields (2003)

An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of cellularity. We...

Multiplicative structures on homotopy spectral sequences II (2003)

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 classical theorem...

Multiplicative structures on homotopy spectral sequences I (2003)

The paper summarizes the construction of pairings on some standard spectral sequences in algebraic topology.

An Atiyah-Hirzebruch spectral sequence for KR-theory (2003)

This mostly expository paper records some basic facts about towers of homotopy fiber sequences. We give a proof that a pairing of towers induces a pairing of associated spectral sequences, for towers...

K-theory and derived equivalences (2002)

We construct a spectral sequence for computing KR-theory, analogous to the spectral sequence relating motivic cohomology to algebraic K-theory.

Weak equivalences of simplicial presheaves (2002)

We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.

Hypercovers and simplicial presheaves (2002)

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 give a more concrete...

Dugger, Daniel, Hollander, Sharon, Isaksen, Daniel C.

We prove that Jardine's model category of simplicial presheaves can be obtained by localizing the `discrete' version at the collection of all hypercovers. One consequence is that the fibrant objects...

DOI: 10.1017/S0305004103007175 Printed in the United Kingdom Hypercovers and simplicial presheaves (2002)

Daniel Dugger, Sharon Hollander, Daniel C. Isaksen

We use hypercovers to study the homotopy theory of simplicial presheaves. The main result says that model structures for simplicial presheaves involving local weak equivalences can be constructed by...

K-Theory And Derived Equivalences (2002)

Hypercovers in topology (2001)

We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.

Combinatorial model categories have presentations (2000)

We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization functors for the...

Universal homotopy theories (2000)

We show that every combinatorial model category can be obtained, up to Quillen equivalence, by localizing a model category of diagrams of simplicial sets. This says that any combinatorial model...