• Corpus ID: 241035482

Motivic stable homotopy theory is strictly commutative at the characteristic

  title={Motivic stable homotopy theory is strictly commutative at the characteristic},
  author={Tom Bachmann},
We show that mapping spaces in the p-local motivic stable category over an Fp-scheme are strictly commutative monoids (whence HZ-modules) in a canonical way. 


The localization theorem for framed motivic spaces
We prove the analog of the Morel–Voevodsky localization theorem for framed motivic spaces. We deduce that framed motivic spectra are equivalent to motivic spectra over arbitrary schemes, and we give
Nilpotence in normed MGL-modules
We establish a motivic version of the May Nilpotence Conjecture: if E is a normed motivic spectrum that satisfies $E \wedge HZ \simeq 0$, then also $E \wedge MGL \simeq 0$. In words, motivic homology
A1-invarinants in Galois cohomology and a claim of Morel
We establish a variant of the splitting principle of Garibaldi-Merkurjev-Serre for invariants taking values in a strictly homotopy invariant sheaf. As an application, we prove the folklore result of
K-theory of valuation rings
We prove several results showing that the algebraic $K$-theory of valuation rings behaves as though such rings were regular Noetherian, in particular an analogue of the Geisser–Levine theorem. We
From algebraic cobordism to motivic cohomology
Let S be an essentially smooth scheme over a eld of characteristic exponent c. We prove that there is a canonical equivalence of motivic spectra over S MGL=(a1;a2;::: )(1=c)' HZ(1=c); where HZ is the
Relations between slices and quotients of the algebraic cobordism spectrum
We prove a relative statement about the slices of the algebraic cobordism spectrum. If the map from MGL to a certain quotient of MGL introduced by Hopkins and Morel is the map to the zero-slice then
Higher Topos Theory
This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the
Motivic infinite loop spaces
We prove a recognition principle for motivic infinite P1-loop spaces over an infinite perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of
Hyperdescent and étale K-theory
We study the etale sheafification of algebraic K-theory, called etale K-theory. Our main results show that etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is