In this paper we establish a universal characterization of higher algebraic K–theory in the
setting of small stable∞–categories. Specifically, we prove that connective algebraic K …

Abstract For N= 5, 6 and 7, using the classification of perfect quadratic forms, we compute
the homology of the Voronoï cell complexes attached to the modular groups SL N (Z) and …

We produce an $ E_\infty $-ring spectrum $ K (\mathbf {Var} _ {/k}) $ whose components
model the Grothendieck ring of varieties (over a field $ k $) $ K_0 (\mathbf {Var} _ {/k}) …

For a finite-dimensional vector space, the common basis complex of is the simplicial
complex whose vertices are the proper non-zero subspaces of, and is a simplex if and only if …

For a multiplicative cohomology theory E, complex orientations are in bijective
correspondence with multiplicative natural transformations to E from complex bordism …

Let K 0 (V k) be the Grothendieck group of k-varieties. Campbell and Zakharevich have
constructed a higher algebraic K-theory spectrum K (V k) such that π 0 K (V k)= K 0 (V k). In …

We prove that the fourth algebraic K-group of the integers is the trivial group, ie, that K 4 (Z)=
0. The argument uses rank-, poset-and component filtrations of the algebraic K-theory …

We interpret different constructions of the algebraic K‐theory of spaces as an instance of
derived Koszul (or bar) duality and also as an instance of Morita equivalence. We relate the …

The Steinberg representation is irreducible Page 1 THE STEINBERG REPRESENTATION IS
IRREDUCIBLE ANDREW PUTMAN and ANDREW SNOWDEN Abstract We prove that the …

Given a special Γ-category 𝒞 satisfying some mild hypotheses, we construct a sequence of
spectra interpolating between the spectrum associated to 𝒞 and the Eilenberg-Mac Lane …