Search results for: John Rognes

Items from 1 to 10 out of 10 results

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Algebraic K-theory of group rings and the cyclotomic trace map

Wolfgang Lück, Holger Reich, John Rognes, Marco Varisco

Advances in Mathematics > 2017 > 304 > C > 930-1020

We prove that the Farrell–Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt–Schneider conjecture holds for cyclotomic fields. This generalizes a result of Bökstedt, Hsiang, and Madsen, and leads to a concrete description of a large direct summand of Kn(Z[G])⊗ZQ in...

article

Localization sequences for logarithmic topological Hochschild homology

John Rognes, Steffen Sagave, Christian Schlichtkrull

Mathematische Annalen > 2015 > 363 > 3-4 > 1349-1398

We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like real and complex topological $$K$$ K -theory.

article

On cyclic fixed points of spectra

Marcel Bökstedt, Robert R. Bruner, Sverre Lunøe-Nielsen, John Rognes

Mathematische Zeitschrift > 2014 > 276 > 1-2 > 81-91

For a finite $$p$$ p -group $$G$$ G and a bounded below $$G$$ G -spectrum $$X$$ X of finite type mod $$p$$ p , the $$G$$ G -equivariant Segal conjecture for $$X$$ X asserts that the canonical map $$X^G \rightarrow X^{hG}$$ X G → X h G , from $$G$$ G -fixed points to $$G$$ G -homotopy fixed points, is a $$p$$...

article

Two-primary algebraic K-theory of pointed spaces

John Rognes

Topology > 2002 > 41 > 5 > 873-926

We compute the mod2 cohomology of Waldhausen's algebraic K-theory spectrum A(*) of the category of finite pointed spaces, as a module over the Steenrod algebra. This also computes the mod2 cohomology of the smooth Whitehead spectrum of a point, denoted Wh ^D ⁱ ^f ^f (*). Using an Adams spectral sequence we compute the 2-primary homotopy groups of these spectra in dimensions *=<18,...

article

Two-primary algebraic K-theory of two-regular number fields

John Rognes, Paul Arne stvr

Mathematische Zeitschrift > 2000 > 233 > 2 > 251-263

Abstract. We explicitly calculate all the 2-primary higher algebraic K-groups of the rings of integers of all 2-regular quadratic number fields, cyclotomic number fields, or maximal real subfields of such. Here 2-regular means that (2) does not split in the number field, and its narrow Picard group is of odd order.

article

The product on topological Hochschild homology of the integers with mod 4 coefficients

John Rognes

Journal of Pure and Applied Algebra > 1999 > 134 > 3 > 211-218

We compute the natural multiplication on mod 4 homotopy for the ring spectrum T(Z) = THH (Z), and its associated natural module action upon the mod2 homotopy.

article

Topological cyclic homology of the integers at two

John Rognes

Journal of Pure and Applied Algebra > 1999 > 134 > 3 > 219-286

The topological Hochschild homology of the integers T(Z)=THH(Z) is an S ¹ -equivalent spectrum. We prove by computation that for the restricted C ₂ -action on T(Z) the fixed points and homotopy fixed points are equivalent, after passing to connective covers and completing at two. By Tsalidis (1994) a similar statement then holds for the action of every cyclic subgroup C ₂ ...

article

Algebraic K-theory of the two-adic integers

John Rognes

Journal of Pure and Applied Algebra > 1999 > 134 > 3 > 287-326

We compute the two-completed algebraic K-groups K _* (< ₂ ) ₂ of the two-adic integers, and determine the homotopy type of the two-completed algebraic K-theory spectrum K(< ₂ ) ₂ . The natural map K(Z) ₂ -> K(<) ₂ is shown to induce an isomorphism modulo torsion in degrees 4k + 1 with k =< 1.

article

Trace maps from the algebraicK-theory of the integers (after Marcel Bo¨kstedt)

John Rognes

Journal of Pure and Applied Algebra > 1998 > 125 > 1-3 > 277-286

Letp be any prime. We consider Bo¨kstedt's topological refinementK(ℤ) → T(ℤ) = THH(ℤ)of the Dennis trace map from algebraicK-theory of the integers to topological Hochschild homology of the integers. This trace map is shown to induce a surjection on homotopy in degree2p − 1, onto the firstP-torsion in the target. Furthermore, Bo¨kstedt's map factors through theS ¹ -homotopy fixed pointsT(ℤ)hS...

article

The fiber of the linearization map A(*) → K(Z)

John R. Klein, John Rognes

Topology > 1997 > 36 > 4 > 829-848

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