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Let $k$ be an algebraically closed field, $l eqoperatorname{char} k$ a prime number, and $X$ a quasi-projective scheme over $k$. We show that the etale homotopy type of the $d$th symmetric power of $X$ is $mathbb Z/l$-homologically equivalent to the $d$th strict symmetric power of the etale homotopy type of $X$. We deduce that the $mathbb Z/l$-local etale homotopy type of a motivic Eilenberg-Mac Lane space is an ordinary Eilenberg-Mac Lane space.
Let $p$ be a prime. We calculate the connective unitary K-theory of the smash product of two copies of the classifying space for the cyclic group of order $p$, using a K{u}nneth formula short exact sequence. As a corollary, using the Bott exact seque
We obtain geometric models for the infinite loop spaces of the motivic spectra $mathrm{MGL}$, $mathrm{MSL}$, and $mathbf{1}$ over a field. They are motivically equivalent to $mathbb{Z}times mathrm{Hilb}_infty^mathrm{lci}(mathbb{A}^infty)^+$, $mathbb{
We introduce and study the homotopy theory of motivic spaces and spectra parametrized by quotient stacks [X/G], where G is a linearly reductive linear algebraic group. We extend to this equivariant setting the main foundational results of motivic hom
We prove a trace formula in stable motivic homotopy theory over a general base scheme, equating the trace of an endomorphism of a smooth proper scheme with the Euler characteristic integral of a certain cohomotopy class over its scheme of fixed point
In this short paper we outline (mostly without proofs) our new approach to the derived category of sheaves of commutative DG rings. The proofs will appear in a subsequent paper. Among other things, we explain how to form the derived intersection of