Florian Ivorra
For a field of characteristic zero, M. Levine has proved that his category of triangulated motives is equivalent to the one constructed by V. Voevodsky. In this paper we show that the strategy of Levine's proof can be applied on every perfect field to the categories of triangulated motives with rational coefficients.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In earlier work (arXiv:0801.0261), we gave a definition of an abelian category of motivic (constructible) sheaves over a base in characteristic zero using Nori's method. This category has Hodge and etale realizations, and is stable under inverse and direct images for projective and constant maps. The goal of this paper is to give a simpler definition of (a slight modification of) the category, and to give an easier proof of the direct image theorem. This paper relies on the previous article for some technical results, but is otherwise self contained.
We study which quadratic forms are representable as the local degree of a map $f : A^n \to A^n$ with an isolated zero at $0$, following the work of Kass and Wickelgren who established the connection to the quadratic form of Eisenbud, Khimshiashvili, and Levine. Our main observation is that over some base fields $k$, not all quadratic forms are representable as a local degree. Empirically the local degree of a map $f : A^n \to A^n$ has many hyperbolic summands, and we prove that in fact this is the case for local degrees of low rank. We establish a complete classification of the quadratic forms…
Motivic Steenrod operations at the characteristic via infinite ramification
本文在特征p处通过无限分叉构造了motivic Steenrod运算，并给出了其在代数循环和晶体检测塔猜想方面的应用。
Using a recent computation of the rational minus part of $SH(k)$ by Ananyevskiy-Levine-Panin, a theorem of Cisinski-Deglise and a version of the Roendigs-Ostvaer theorem, rational stable motivic homotopy theory over an infinite perfect field of characteristic different from 2 is recovered in this paper from finite Milnor-Witt correspondences in the sense of Calmes-Fasel.
We show that the Conjecture of Voevodsky concerning slices of the algebraic cobordism spectrum MGL implies a general statement about the slices of motivic Landweber spectra. In particular it confirms the possible approach suggested by Voevodsky for the computation of the slices of the homotopy algebraic K-theory spectrum KGL via a Conner-Floyd isomorphism complementing Levine's unconditional proof of these slices over perfect fields. A similar result, and Voevodsky's conjecture over fields of char. 0, are also announced by Hopkins-Morel.
In characteristic 0 there are essentially two approaches to the conjectural theory of mixed motives, one due to Nori and the other one due to, independently, Hanamura, Levine, and Voevodsky. Although these approaches are apriori quite different it is expected that ultimately they can be reduced to one another. In this article we provide some evidence for this belief by proving that their associated motivic Galois groups are canonically isomorphic.
In this paper, we study twisted algebraic $K$-theory from a motivic viewpoint. For a smooth variety $X$ over a field of characteristic zero and an Azumaya algebra $\mathcal{A}$ over $X$, we construct the $\mathcal{A}$-twisted motivic spectral sequence, by computing the slices of the motivic twisted algebraic $K$-theory spectrum as a twisted form of motivic cohomology. This generalizes previous results due to Kahn-Levine where $\mathcal{A}$ is assumed to be pulled back from a base field. Our methods use interaction between the slice filtration and birational geometry. Along the way, we prove a …
Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space
本文借助 Levine 的动机虚基本类定义 R 上 P^3 的动机 DT 不变量，证明奇数阶为零并算出前三个偶数阶值，进而提出一般情形猜想。
Motivic Euler Characteristic of Nearby Cycles and a Generalized Quadratic Conductor Formula
本文通过半稳定约化的层计算 Ayoub 邻近周期谱的动机欧拉示性数，证明 Levine–Pepin Lehalleur–Srinivas 超曲面导子公式的局部性，并将其推广到多奇点情形。
The quadric $\operatorname{Q}_{2n}$ is the ${\mathbb Z}$-scheme defined by the equation $\sum_{i=1}^n x_i y_i = z(1-z)$. We show that $\operatorname{Q}_{2n}$ is a homogeneous space for the split reductive group scheme $\operatorname{SO}_{2n+1}$ over ${\mathbb Z}$. The quadric $\operatorname{Q}_{2n}$ is known to have the ${\mathbb A}^1$-homotopy type of a motivic sphere and the identification as a homogeneous space allows us to give a characteristic independent affine representability statement for motivic spheres. This last observation allows us to give characteristic independent comparison re…
Let G be a split semisimple linear algebraic group over a field k0. Let E be a G-torsor over a field extension k of k0. Let h be an algebraic oriented cohomology theory in the sense of Levine-Morel. Consider a twisted form E/B of the variety of Borel subgroups G/B over k. Following the Kostant-Kumar results on equivariant cohomology of flag varieties we establish an isomorphism between the Grothendieck groups of the h-motivic subcategory generated by E/B and the category of finitely generated projective modules of certain Hecke-type algebra H which depends on the root datum of G, on the torsor…
The motivic fundamental groupoid at tangential basepoints
本文通过构造切点基点的动机基本群oid，扩展了Deligne等人之前的工作，利用对数几何语言编码光滑变种的切点基点，并展示了其周期由正则化的迭代积分给出。
This paper proves the Beilinson-Soul{é} vanishing conjecture for motives attached to the moduli spaces of curves of genus 0 with n marked points. As part of the proof, it is also proved that these motives are mixed Tate. As a consequence of Levine's work, one obtains then well defined categories of mixed Tate motives over the moduli spaces of curves . It is shown that morphisms between moduli spaces forgetting marked points and embedding as boundary components induce functors between those categories and how tangential bases points fit in these functorialities. Tannakian formalism attaches gro…
Let $k$ be a field with resolution of singularities, and $X$ a separated $k$-scheme of finite type with structure map $g$. We show that the slice filtration in the motivic stable homotopy category commutes with pullback along $g$. Restricting the field further to the case of characteristic zero, we are able to compute the slices of Weibel's homotopy invariant $K$-theory extending the result of Levine, and also the zero slice of the sphere spectrum extending the result of Levine and Voevodsky. We also show that the zero slice of the sphere spectrum is a strict cofibrant ring spectrum $\mathbf{H…
Cellular $\mathbb A^1$-homology and the motivic version of Matsumoto's theorem
本文定义了适用于域上光滑概形的胞腔 $\mathbb A^1$-同调，通过显式计算确定了任意域上分裂约化群的 $\mathbb A^1$-基本群，从而获得了 Matsumoto 定理的动形版本，并统一推广了相关的中心扩张与同伦群结果。
This paper is dedicated to the study of the kernel of the "compact motivization" functor $M_{k}^c:SH^c(k)\to DM^c(k)$ (i.e., we try to describe those compact objects of $SH(k)$ whose associated motives vanish. Moreover, we study the question when the $m$-connectivity of $M^c_{k}(E)$ ensures the $m$-connectivity of $E$ itself (with respect to the corresponding homotopy t-structures). We prove that the kernel of $M_{k}^c$ vanishes and the corresponding "connectivity detection" statement is also valid if and only if $k$ is a non-orderable field; this is an easy consequence of the corresponding re…
Hypercomplete étale framed motives and comparison of stable homotopy groups of motivic spectra and étale realizations over a field
本文在 motivic 同伦论框架下，构造$l$-进完备超完备平展标架motive理论，证明相关函子的交换性与识别原理，推导平展局部同构，并给出Levine比较同构及其代数闭域推广的新证明，结果适用于任意基域。
Quadratic Euler Characteristic of Symmetric Powers of Curves
本文借助 Levine–Raksit 动机 Gauss–Bonnet 定理计算非特征二域上光滑射影曲线对称幂的二次 Euler 示性数，并证明 Pajwani–Pál 幂结构在特征零下给出相应紧支撑 $\mathbb{A}^1$-Euler 示性数。
We compare various groups of 0-cycles on quasi-projective varieties over a field. As applications, we show that for certain singular projective varieties, the Levine-Weibel Chow group of 0-cycles coincides with the corresponding Friedlander-Voevodsky motivic cohomology. We also show that over an algebraically closed field of positive characteristic, the Chow group of 0-cycles with modulus on a smooth projective variety with respect to a reduced divisor coincides with the Suslin homology of the complement of the divisor. We prove several generalizations of the finiteness theorem of Saito and Sa…
We describe algebraically defined cohomological and homological Albanese and Picard 1-motives (or mixed motives) of any algebraic variety in characteristic zero, generalizing the classical Albanese and Picard varieties. We compute Hodge, l-adic and De Rham realizations proving Deligne's conjecture for the concerned mixed Hodge structures. We investigate functoriality, universality, homotopical invariance and invariance under formation of projective bundles. We compare our cohomological and homological 1-motives for normal schemes. For proper schemes, we obtain an Abel-Jacobi map from the (Levi…
This book discusses the construction of triangulated categories of mixed motives over a noetherian scheme of finite dimension, extending Voevodsky's definition of motives over a field. In particular, it is shown that motives with rational coefficients satisfy the formalism of the six operations of Grothendieck. This is achieved by studying descent properties of motives, as well as by comparing different presentations of these categories, following and extending insights and constructions of Deligne, Beilinson, Bloch, Thomason, Gabber, Levine, Morel, Voevodsky, Ayoub, Spitzweck, Röndigs, Østvær…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。