相关论文: On weight truncations in the motivic setting
Using the trivial fiber topology we describe motivic $\infty$-loop spaces and fibrant replacements in the motivic stable homotopy category $\mathbf{SH}_{\mathbb{A}^1,\mathrm{Nis}}(B)$ defined over one-dimensional base schemes $B$.
We prove that $\mathrm{SO}(3)$ modular functors in genus $0$ have geometric origin and support integral variations of Hodge structures for any odd level $r$ and $r$-th root of unity $\zeta_r\in\mathbb{C}$. We identify the TQFT intersection…
We investigate the combinatorial analogues, in the context of normal surfaces, of taut and transversely measured (codimension 1) foliations of 3-manifolds. We establish that the existence of certain combinatorial structures, a priori weaker…
We describe a new method for constructing a weight structure $w$ on a triangulated category $C$. For a given $C$ and $w$ it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of…
In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We…
We formalize the concept of sheaves of sets on a model site by considering variables thereof, or motifs, and we construct functorially defined derived algebraic stacks from them, thereby eliminating the necessity to choose derived…
We define and study Gysin morphisms on mixed motives over a perfect field. Our construction extends the case of closed immersions, already known from results of Voevodsky, to arbitrary projective morphisms. We prove several classical…
We develop the theory of truncated wedge schemes, a higher dimensional analog of jet schemes. We prove some basic properties and give an irreducibility criterion for truncated wedge schemes of a locally complete intersection variety…
We prove that the metric of a general holographic spacetime can be reconstructed (up to an overall conformal factor) from distinguished spatial slices - "light-cone cuts" - of the conformal boundary. Our prescription is covariant and…
We construct a quasi-categorically enhanced Grothendieck six-functor formalism on schemes of finite type over the complex numbers. In addition to satisfying many of the same properties as M. Saito's derived categories of mixed Hodge…
We compute the influence action for a system perturbatively coupled to a linear scalar field acting as the environment. Subtleties related to divergences that appear when summing over all the modes are made explicit and clarified. Being…
Given a complex smooth algebraic variety X, we compute the generating function of the stringy motives of its symmetric powers as a function of motive of X. In dimension two we recover the Goettsche formulas for Hilbert schemes. We use the…
The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible…
We study certain triangulated categories of $K$-motives $DK(-)$ over a wide class of base schemes, and define certain "weights" for them. We relate the weights of particular $K$-motives to (negative) homotopy invariant $K$-groups (tensored…
In this paper we define the triangulated category of motives over a simplicial scheme. The morphisms between the Tate objects in this category compute the motivic cohomology of the underlying scheme. In the last section we consider the…
Let $k$ be a field of characteristic zero with a fixed embedding $\sigma:k\hookrightarrow \mathbb{C}$ into the field of complex numbers. Given a $k$-variety $X$, we use the triangulated category of \'etale motives with rational coefficients…
We produce many new complete, constant Q-curvature metrics on finitely punctured spheres by gluing together known examples. In our construction we truncate one end of each summand and glue the two summands together "end-to-end," where we've…
Given a perfect field of exponential characteristic $e$ and a functor $f:\mathcal A\to\mathcal B$ between symmetric monoidal strict $V$-categories of correspondences satisfying the cancellation property such that the induced morphisms of…
The purpose of this article is to study conservativity in the context of triangulated categories equipped with a weight structure. As application, we establish (weight) conservativity for the restriction of the (generic) l-adic realization…
Given a right adjoint functor between triangulated categories and an object in the target category, we show that the unit map of adjunction on that object is a split monomorphism if and only if the object belongs to the additive closure of…