Related papers: Unwinding the relative Tate diagonal
For a smooth and proper scheme over an artinian local ring with ordinary reduction over the perfect residue field we prove - under some general assumptions - that the relative de Rham-Witt spectral sequence degenerates and the relative…
We study Tate-Hochschild homology and cohomology for a two-sided Noetherian Gorenstein algebra. These (co)homology groups are defined for all degrees, non-negative as well as negative, and they agree with the usual Hochschild (co)homology…
We prove that for a homologically smooth and proper DG algebra over a field of characteristic 0, the Hodge-to-de Rham spectral sequence degenerates. This has been conjectured by M. Kontsevich and Y. Soibelman arXiv:math/0606241 and proved…
We apply the methods of Heegaard Floer homology to identify topological properties of complex curves in the complex projective plane. As one application, we resolve an open conjecture that constrains the Alexander polynomial of the link of…
We show that the graph TQFT for Heegaard Floer homology satisfies a strong version of Atiyah's duality axiom for a TQFT. As an application, we compute some Heegaard Floer mixed invariants of 4-dimensional mapping tori in terms of Lefschetz…
Let $X$ be a smooth irreducible projective variety over a field $\mathbf{k}$ of dimension $d.$ Let $\tau: \mathbb{Q}_l\to \mathbb{C}$ be any field embedding. Let $f: X\to X$ be a surjective endomorphism. We show that for every…
We study the spectral sequence that one obtains by applying mod 2 homology to the Goodwillie tower which sends a spectrum X to the suspension spectrum of its 0th space X_0. This converges strongly to H_*(X_0) when X is 0-connected. The E^1…
Let $(S,L)$ be a Lie-Rinehart algebra such that $L$ is $S$-projective and let $U$ be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of $U$ with values on a…
We identify the topological Hochschild homology (THH) of the Thom spectrum associated to an E_\infty classifying map X -> BG, for G an appropriate group or monoid (e.g. U, O, and F). We deduce the comparison from the observation of McClure,…
We explain how a simple twisting of the notion of spectral triple allows to incorporate type III examples, such as those arising from the transverse geometry of codimension one foliations. Since the twisting of the commutators turns the…
We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\'ar for classical expansion of bounded…
We combine the theory of traces in homotopical algebra with sheaf theory in derived algebraic geometry to deduce general fixed point and character formulas. The formalism of dimension (or Hochschild homology) of a dualizable object in the…
In this note, we investigate homomorphisms from the periodic Floer homology (PFH) to the quantitative Heegaard Floer homology. We call the homomorphisms closed-open morphisms. Under certain assumptions on the Lagrangian link, we first…
We show that bordered Heegaard Floer homology detects incompressible surfaces and bordered-sutured Floer homology detects partly boundary parallel tangles and bridges, in natural ways. For example, there is a bimodule Lambda so that the…
We compare two different types of mapping class invariants: the Hochschild homology of an $A_\infty$ bimodule coming from bordered Heegaard Floer homology, and fixed point Floer cohomology. We first compute the bimodule invariants and their…
We extend the computations in [AGM1, AGM2, AGM3] to find the cohomology in degree five of a congruence subgroup Gamma of SL(4,Z) with coefficients in a field K, twisted by a nebentype character eta, along with the action of the Hecke…
We show that any open 2-dimensional topological field theory valued in a symmetric monoidal $\infty$-category (with suitable colimits) extends canonically to an open-closed field theory whose value at the circle is the Hochschild homology…
We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so called (derived) Hochschild complex of a morphism; the…
Given a filtration of a commutative monoid $A$ in a symmetric monoidal stable model category $\mathcal{C}$, we construct a spectral sequence analogous to the May spectral sequence whose input is the higher order topological Hochschild…
In this paper, we construct a Real equivariant version of the B\"okstedt spectral sequence which takes inputs in the theory of Real Hochschild homology developed by Angelini-Knoll, Gerhardt, and Hill and converges to the equivariant…