Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

We provide conditions on a monoidal model category M so that the category of commutative
monoids in M inherits a model structure from M in which a map is a weak equivalence or …

We define a derived version of Mazur's Galois deformation ring. It is a pro-simplicial ring R
classifying deformations of a fixed Galois representation to simplicial coefficient rings; its …

We give conditions on a monoidal model category M and on a set of maps C so that the
Bousfield localization of M with respect to C preserves the structure of algebras over various …

We provide foundations for dealing with the equivariant structure of" smash powers" of
commutative orthogonal ring spectra. The category of commutative orthogonal ring spectra …

In this paper we extend equivariant infinite loop space theory to take into account
multiplicative norms: For every finite group $ G $, we construct a multiplicative refinement of …

After the first heuristic ideas about “the field of one element” F1 and “geometry in
characteristics 1”(J. Tits, C. Deninger, M. Kapranov, A. Smirnov et al.), were developed …

We initiate the homotopical study of racks and quandles, two algebraic structures that
govern knot theory and related braided structures in algebra and geometry. We prove …

Algebraic K-theory draws its importance from its effective codification of a mathematical
phenomenon which occurs in as separate parts of mathematics as number theory, geometric …

This comprehensive text focuses on the homotopical technology in use at the forefront of
modern algebraic topology. Following on from a standard introductory algebraic topology …