Related papers: The Morel-Voevodsky localization theorem in spectr…

Using methods developed by Franke, we obtain algebraic classification results for modules over certain symmetric ring spectra ($S$-algebras). In particular, for any symmetric ring spectrum $R$ whose graded homotopy ring $\pi_*R$ has graded…

We construct smooth presentations of algebraic stacks that are local epimorphisms in the Morel-Voevodsky $\mathbb{A}^1$-homotopy category. As a consequence we show that the motive of a smooth stack (in Voevodsky's triangulated category of…

This paper introduces the trivial fiber topology on schemes. For one-dimensional base schemes, we use it to describe fibrant replacements in the stable motivic homotopy category and motivic infinite loop spaces. We also extend the…

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…

Under a certain normalization assumption we prove that the $\Pro^1$-spectrum $\mathrm{BGL}$ of Voevodsky which represents algebraic $K$-theory is unique over $\Spec(\mathbb{Z})$. Following an idea of Voevodsky, we equip the…

The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In this paper, we study the relative Baum-Connes assembly map…

Quillen's algebraic K-theory is reconstructed via Voevodsky's algebraic cobordism. More precisely, for a ground field k the algebraic cobordism P^1-spectrum MGL of Voevodsky is considered as a commutative P^1-ring spectrum. There is a…

Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $\theta$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_\theta(G) \subseteq V$ of semistable points. We give necessary,…

We provide an explicit formula for localizing $A^1$-homotopy invariants of topological Fukaya categories of marked surfaces. Following a proposal of Kontsevich, this differential $\mathbb Z$-graded category is defined as global sections of…

In this work we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The Weyl conformal algebra is the universal associative conformal envelope of the Virasoro Lie conformal…

We prove that the $\infty$-category of $\mathrm{MGL}$-modules over any scheme is equivalent to the $\infty$-category of motivic spectra with finite syntomic transfers. Using the recognition principle for infinite $\mathbb{P}^1$-loop spaces,…

We characterize ring spectra morphisms from the algebraic cobordism spectrum $\QTR{Bbb}{MGL}$ (\QCITE{cite}{}{Vo1}) to an oriented spectrum $\QTR{Bbb}{E}$ (in the sense of Morel \QCITE{cite}{}{Mo}) via formal group laws on the…

Mostow's Decomposition Theorem is a refinement of the polar decomposition. It states the following. Let G be a compact connected semi-simple Lie group with Lie algebra g. Given a subspace h of g such that [X, [X, Y]] belongs to h for all X…

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras A_i\in V, such that some finitely generated subalgebra S \subseteq A is dense in A under the inverse limit of the discrete topologies…

The symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group ring $A = k[\Gamma]$, the symmetric homology is related to…

Let $D, \Omega_1, ..., \Omega_m$ be irreducible bounded symmetric domains. We study local holomorphic maps from $D$ into $\Omega_1 \times... \Omega_m$ preserving the invariant $(p, p)$-forms induced from the normalized Bergman metrics up to…

C. Weibel and Thomason-Trobaugh proved (under some assumptions) that algebraic K-theory with coefficients is A1-homotopy invariant. In this article we generalize this result from schemes to the broad setting of dg categories. Along the way,…

We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov-Witten classes of all smooth complete…

We prove that certain involutions defined by Vogell and Burghelea-Fiedorowicz on the rational algebraic $K$-theory of spaces coincide. This gives a way to compute the positive and negative eigenspaces of the involution on rational homotopy…

We define algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra g. The new slices are transversal to the conjugacy classes in an algebraic group G with Lie algebra g. These slices…