60 research outputs found
Comparing cyclotomic structures on different models for topological Hochschild homology
No full textC. Malkiewich was supported by an AMS Simons Travel Grant. I. Patchkoria was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and by the German Research Foundation Schwerpunktprogramm 1786. E. Dotto and I. Patchkoria were supported by the Hausdorff Center for Mathematics at the University of Bonn. Acknowledgements The authors would like to thank Andrew Blumberg, Amalie Høgenhaven, Michael Mandell, Kristian Moi, Thomas Nikolaus, Stefan Schwede and Martin Stolz for helpful conversations related to this project. Moreover, the authors would like to thank the referee for a detailed report that helped to substantially improve this paper. C. Malkiewich and C. Woo thank the Hausdorff Research Institute for Mathematics in Bonn for their hospitality while the draft of this paper was finalized.Peer reviewe
RIGIDITY IN EQUIVARIANT STABLE HOMOTOPY THEORY
No full textFor any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all "higher order structure'' of the 2-local G-equivariant stable homotopy category, such as the equivariant homotopy types of function G-spaces. The theorem can be seen as an equivariant version of Schwede's rigidity theorem at the prime 2
On the de Rham–Witt Complex over Perfectoid Rings
No full textAcknowledgments The 1st author is very grateful to Lars Hesselholt, who introduced and explained many aspects of this project to him. (The project began around 2014 when the 1st author was a postdoc of Lars Hesselholt at the University of Copenhagen.) The 1st author would also like to especially thank Bhargav Bhatt for assistance at many different points, especially during a visit to the University of Michigan. Furthermore, both authors thank Johannes Anschütz, Bryden Cais, Dustin Clausen, Elden Elmanto, Kiran Kedlaya, Arthur-César Le Bras, Thomas Nikolaus, Peter Scholze, and David Zureick-Brown for useful conversations regarding this paper. The authors also thank the anonymous referee of an earlier version of this paper; the referee provided careful feedback and many suggestions for improvement, especially in Section 7. Both authors thank the Department of Mathematical Sciences of the University of Copenhagen for its hospitality and pleasant working environment.Peer reviewe
Rigidity and exotic models for v1-local G-equivariant stable homotopy theory
No full textWe prove that the v1-local G-equivariant stable homotopy category for G a finite group has a unique G-equivariant model at p=2. This means that at the prime 2 the homotopy theory of G-spectra up to fixed point equivalences on K-theory is uniquely determined by its triangulated homotopy category and basic Mackey structure. The result combines the rigidity result for K-local spectra of the second author with the equivariant rigidity result for G-spectra of the first author. Further, when the prime p is at least 5 and does not divide the order of G, we provide an algebraic exotic model as well as a G-equivariant exotic model for the v1-local G-equivariant stable homotopy category, showing that for primes p≥5 equivariant rigidity fails in general
Chromatic congruences and Bernoulli numbers
No full textFor every natural number and a fixed prime , we prove a new congruence for the orbifold Euler characteristic of a group. The -adic limit of these congruences as tends to infinity recovers the Brown-Quillen congruence. We apply these results to mapping class groups and using the Harer-Zagier formula we obtain a family of congruences for Bernoulli numbers. We show that these congruences in particular recover classical congruences for Bernoulli numbers due to Kummer, Voronoi, Carlitz, and Cohen.22 page
Adams spectral sequences and Franke's algebraicity conjecture
No full textTo any well-behaved homology theory we associate a derived -category
which encodes its Adams spectral sequence. As applications, we prove a
conjecture of Franke on algebraicity of certain homotopy categories and
establish homotopy-coherent monoidality of the Adams filtration.Comment: Fixed typos; several minor corrections and updates; 114 page
- …
