Syntomic cohomology and real topological cyclic homology

2023/11/11 by Doosung Park, Park, Doosung · 1 voice
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2311.06593

Abstract

We define the motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions of syntomic cohomology. As an application, assuming a real refinement of the Dundas--Goodwillie--McCarthy theorem, we compute the the RO(ℤ/2)-graded homotopy groups of KR(\mathbbF_p[x]/x^e;ℤ_p), and we compute the equivariant slices of Σ² τ_{≥ 1}KR(ℤ/pⁿ;ℤ_p).

Citations

• On the nonexistence of elements of Kervaire invariant one

Discussions

• Doosung Park Syntomic cohomology and real topological cyclic cohomology. (arXiv:2311.06593v1 [math.KT]) http://arxiv.org/abs/2311.06593 [bsky, 0 points, 0 comments]

Related

• On the equivariant motivic filtration of the topological Hochschild homology of polynomial algebras
• Algebraic K-theory of real topological K-theory
• A motivic filtration on the topological cyclic homology of commutative ring spectra
• Topological Hochschild homology and integral p-adic Hodge theory
• Real syntomic cohomology