相关论文: String bordism and chromatic characteristics

Gross and Hopkins have proved that in chromatic stable homotopy, Spanier-Whitehead duality nearly coincides with Brown-Comenetz duality. Our goal is to give a conceptual interpretation for this phenomenon in terms of the Gorenstein…

We record various properties of twisted Becker-Gottlieb transfer maps and study their multiplicative properties analogous to Becker-Gottlieb transfer. We show these twisted transfer maps factorise through Becker-Schultz-Mann-Miller-Miller…

Using intersection theory in the context of Hilbert manifolds and geometric homology we show how to recover the main operations of string topology built by M. Chas and D. Sullivan. We also study and build an action of the homology of…

We study topological properties of the correspondence of prime spectra associated to a noncommutative ring homomorphism R -> S. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski…

We establish a "second vanishing theorem" for local cohomology modules over regular rings of unramified mixed characteristic, which relates the connectedness of the spectrum of a ring with the vanishing of local cohomology. Applying this,…

Using a previous classification result on symmetric additive 2-cocycles, we collect a variety of facts about the Lubin-Tate cohomology of formal groups to compute the 2-primary component of the scheme of symmetric multiplicative 2-cocycles.…

Let {D_x} be a family of unbounded self-adjoint Fredholm operators representing an element of K^1(M). Consider the first two components of the Chern character of the family. It is known that these correspond to the spectral flow of the…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove…

We give a higher-algebraic interpretation of complex orientations of ring spectra as "$\mathbb{E}_2$ strictifications" of the identity element. We show that higher strictifications do not exist for most ring spectra of interest in chromatic…

We develop a general theory of higher semiadditive Fourier transforms that includes both the classical discrete Fourier transform for finite abelian groups at height $n=0$, as well as a certain duality for the $E_n$-(co)homology of…

We study a family of subrings, indexed by the natural numbers, of the mod-p cohomology of a finite group G. These subrings are based on a family of v_n-periodic complex oriented cohomology theories and are constructed as rings of…

We show that the 2-local splitting of spin$^c$ bordism by Anderson--Brown--Peterson and Stong refines to a $C_2$-equivariant map in the category of spectra with $C_2$-action from Real spin bordism to a sum of (higher) connective covers of…

We construct a family of exactly solvable spin models that illustrate a novel mechanism for fractionalization in topologically ordered phases, dubbed the string flux mechanism. The essential idea is that an anyon of a topological phase can…

The 8-periodic theory that comes from the KO-theory of the mod 2 Moore space is the same as the real first Morava K-theory obtained from the homotopy fixed points of the Z/(2) action on the first Morava K-theory. The first Morava K-theory,…

The Hochschild cohomology of a differential graded algebra, or a differential graded category, admits a natural map to the graded center of its homology category: the characteristic homomorphism. We interpret it as an edge homomorphism in a…

Let $k$ be a field of characteristic zero and I an ideal defining an arrangement of linear subspaces in the affine space $A^n_k$. We compute the D-module theoretic characteristic cycle of the local cohomology modules $H^r_I(k[x_1,...,x_n])$…

In this note, for each odd prime $p$, we show that the orders of the $KU$-local homotopy groups of the mod $p$ Moore spectrum are equal to denominators of special values of certain quotients of Dedekind zeta-functions of totally real number…

We generalize Quillen's $F$-isomorphism theorem, Quillen's stratification theorem, the stable transfer, and the finite generation of cohomology rings from finite groups to homotopical groups. As a consequence, we show that the category of…

This paper introduces a new cohomology theory for schemes of finite type over an arithmetic ring. The main motivation for this Arakelov-theoretic version of motivic cohomology is the conjecture on special values of $L$-functions and zeta…