Bruno Kahn
We extend results of Colliot-Thélène and Raskind on the $\mathcal{K}_2$-cohomology of smooth projective varieties over a separably closed field $k$ to the étale motivic cohomology of smooth, not necessarily projective, varieties over $k$. Some consequences are drawn, such as the degeneration of the Bloch-Lichtenbaum spectral sequence for any field containing $k$.
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
Divisibility phenomena in motivic Bloch--Ogus theory
本文研究了光滑项目ive变种上的动机Bloch-Ogus理论中的可除现象，证明了函数域的MilnorK群中无分歧类的子群包含在n可除元素子群中，并推广到任意双度数的动机上同调，进一步证明当k为有限或可分闭域且l为k中可逆素数时，X的动机上同调的Bloch-Ogus滤波中除了最后一步外都是l可除的，且推广到任意准项目ivek-方案。
Parshin's conjecture and motivic cohomology with compact support
讨论了Parshin关于有限域上有理K-理论的猜想及其对紧支集的动机上同调的意义.
We prove that, over a perfect field, Bredon motivic cohomology can be computed by Suslin-Friedlander complexes of equivariant equidimensional cycles. Partly based on this result we completely identify Bredon motivic cohomology of a quadratically closed field and of a euclidian field in weights 1 and $σ$. We also prove that Bredon motivic cohomology of an arbitrary field in weight 0 with integer coefficients coincides (as abstract groups) with Bredon cohomology of a point.
The Gm-equivariant Motivic Cohomology of Stiefel Varieties
我们推导出一个版本的Rothenberg-Steenrod，光纤到基地，谱序列的上同调理论表示模型类别的单纯预层。然后利用这个谱序列计算了具有一般G_m作用的一般线性群的等变模上同调，这与等变高阶Chow群的模上同调是一致的.作为推论，推导出具有一般Gm作用的Stiefel簇的一些等变动机上同调。
Weil cohomology theories and their motivic Hopf algebroids
本文研究代数几何与刚性解析几何中一般Weil上同调理论，用动机理论给出三种等价视角，构造推广的动机Hopf代数胚，并证明经典Weil上同调对应的动机Hopf代数胚的连通性。
We prove that for a finitely generated field over an infinite perfect field k, and for any integer n, the (n,n)-th MW-motivic cohomology group identifies with the n-th Milnor-Witt K-theory group of that field
We construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers. For the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective. Showing that a suitable Betti--de Rham realization of 1-motives is fully faithful we can verify this period conjecture in several cases. The divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical Grothendieck period conjecture for algebraic cycles on smooth and proper schemes. Th…
Oriented Cohomology and Motivic Decompositions of Relative Cellular Spaces
对于一个定向上同调理论A和一个相对胞腔空间X，我们将X的A-模分解为底空间的扭曲模的直和。我们还得到了X的A-上同调的相应分解。应用它们，可以计算A（X），其中X是迷向投射齐次簇，A表示代数K理论，动机上同调或代数协边MGL.
$\mathbb{A}^1$-invariant motivic cohomology of schemes
本文在任意拟紧拟分离概形上实现了Voevodsky的$\mathbb{A}^1$-不变动机上同调纲领，引入了通过Atiyah--Hirzebruch谱序列与同伦$K$-理论关联的理论，并证明了切片相关猜想。
The Motivic Cohomology of Stiefel Varieties
本文的主要结果是计算了n个秩为m的\times m-矩阵簇的动机上同调，包括环的结构和约化幂运算的作用.论证通过比较一般线性群-方案与具有不相交基点的射影n - 1-空间的A1-等价空间的Tate悬挂来进行。
We construct an algebraic-cycle based model for the motivic cohomology on the category of schemes of finite type over a field, where schemes may admit arbitrary singularities and may be non-reduced. We show that our theory is functorial on the category, that it detects nilpotence, and that its restriction to the subcategory of smooth schemes agrees with the pre-existing motivic cohomology theory, which is the higher Chow theory of S. Bloch (Adv. Math., 1986). A few structures and applications are discussed.
BY using Green-Griffiths' results on tangent spaces to algebraic cycles [4], we study the tangent space to $CH^{2}(X,1)$, where $X$ is a nonsingular projective curve over a field $k$ of characteristic $0$.
For any cohomology theory $H$ that can be factorized through (the Morel-Voevodsky's triangulated motivic homotopy category) $SH^{S^1}(k)$ we establish the $SH^{S^1}(k)$-functoriality of coniveau spectral sequences for $H$. We also prove: for any affine essentially smooth semi-local $S$ the Cousin complex for $H^*(S)$ splits; if $H$ also factorizes through $SH^+(k)$ or $DM(k)$, then this is also true for any primitive $S$. Moreover, the cohomology of such an $S$ is a direct summand of the cohomology of any its open dense subscheme. This is a vast generalization of the results of a previous pape…
We discuss the structure of integral etale motivic cohomology groups of smooth and projective schemes over algebraically closed fields, finite fields, local fields, and arithmetic schemes.
Arakelov motivic cohomology II
我们证明了第一部分所做的构造推广了它们的经典对应：首先，经典Beilinson调节器是由从$BGL$到Deligne上同调谱的抽象Chern类映射导出的.其次，Arakelov动机上同调是算术$K$ -理论和算术Chow群的推广.最后，我们给出了高度配对的概念解释：它是由动机同调和Arakelov动机上同调的自然配对给出的。
A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category by a $ϕ$-torsion spectrum with $ϕ\in\mathrm{GW}(k)$ of rank coprime to the (exponential) characteristic of the base field $k$. It is shown that the values of such cohomology theories at an essentially smooth Henselian ring and its residue field coincide. The result is applicable to cohomology theories representable by $n$-torsion spectra as well as to the one…
Bredon motivic cohomology of the complex numbers
本文在复数域上计算了$C_2$-等变Bredon母题上同调环，并利用刚性将Suslin的经典结果推广到等变母题框架。
We build a ring spectrum representing Milnor-Witt motivic cohomology, as well as its étale local version and show how to deduce out of it three other theories: Borel-Moore homology, cohomology with compact support and homology. These theories, as well as the usual cohomology, are defined for singular schemes and satisfy the properties of their motivic analog (and more), up to considering more general twists. In fact, the whole formalism of these four theories can be functorially attached to any ring spectrum, giving finally maps between the Milnor-Witt motivic ones to the classical motivic one…
Motivic cohomology of the complement of hyperplane arrangements
本文给出了超平面排列的补的运动上同调环的一个表示，超平面排列被认为是基域的运动上同调环上的代数。
We discuss duality pairings on integral étale motivic cohomology groups of regular and proper schemes over algebraically closed fields, local fields, finite fields, and arithmetic schemes.
On Frobenius rigidity for motivic cohomology
该研究探讨光滑真代数簇的两类上同调在基域扩张下的性质，证明有限系数下弗罗贝尼乌斯纤维与基域无关，补充了特征处动机上同调的相关结论。
Due to the work of many authors in the last decades, given an algebraic orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer), one can construct its orbifold Chow ring and orbifold Grothendieck ring, and relate them by the orbifold Chern character map, generalizing the fundamental work of Chen-Ruan on orbifold cohomology. In this paper, we extend this theory naturally to higher Chow groups and higher algebraic K-theory, mainly following the work of Jarvis-Kaufmann-Kimura and Edidin-Jarvis-Kimura.
In this paper, we present a general approach to establish motivic cohomology and build part of its six operations formalism. Applying this together with symplectic orientation on MW-motivic cohomology, we discuss the embedding theorem of effective Chow-Witt motives.
A Serre-type spectral sequence for motivic cohomology
本文构造了动机构上同调的Serre型谱序列，并将其应用于射影一般线性群Nisnevich分类空间的动机构上同调计算，从而给出Severi-Brauer簇动机的显式描述。
We examine the slice spectral sequence for the cohomology of singular schemes with respect to various motivic T-spectra, especially the motivic cobordism spectrum. When the base field k admits resolution of singularities and X is a scheme of finite type over k, we show that Voevodsky's slice filtration leads to a spectral sequence for MGL(X) whose terms are the motivic cohomology groups of X defined using the cdh-hypercohomology. As a consequence, we establish an isomorphism between certain geometric parts of the motivic cobordism and motivic cohomology of X. A similar spectral sequence for th…
Bredon motivic cohomology of the real numbers
本文在实数域上以 $\Z/2$-系数计算 $C_2$-等变 Borel 动机上同调环与 Bredon 动机上同调群，证明其为点空间 $RO(C_2\times C_2)$-分次 Bredon 上同调环的真子环，并推广至任意实闭域。
On motivic cohomology with Z/l coefficients
本文证明了一个关于动机上同调和标准上同调的Bloch-Kato猜想。这是一个更正版本的文件与相同的标题张贴较早。
We introduce a new algebraic-cycle model for the motivic cohomology theory of truncated polynomials $k[t]/(t^m)$ in one variable. This approach uses ideas from the deformation theory and non-archimedean analysis, and is distinct from the approaches via cycles with modulus. We compute the groups in the Milnor range when the base field is of characteristic $0$, and prove that they give the Milnor $K$-groups of $k[t]/(t^m)$, whose relative part is the sum of the absolute Kähler differential forms.
Reduced power operations in motivic cohomology
本文构造了一个类似于Steenrod算子的运动上同调算子，并证明了它们的基本性质，包括Cartan公式、Adem关系和特征类关系.
Motivic cohomology of mixed characteristic schemes
本文为拟紧拟分离概形引入一种动机上同调理论，推广了Elmanto--Morrow的构造，利用拓扑循环同调上的整体滤过提供导出de Rham与合成上同调的整数细化，并满足与étale上同调及非连通代数$K$-理论的关系。
Karoubi's Construction for Motivic Cohomology Operations
我们利用Karoubi在motivic情形下的一个类似构造，给出了motivic上同调的一些上同调运算.我们证明了这些操作的许多属性，我们表明，他们一致，一些非零常数，减少动力上同调最初由Voevodsky构建的功率操作。我们的建设Voevodsky的关系，粗略地说，是一个不动点集，其相关的同伦不动点集。
Weibel vanishing and the projective bundle formula for mixed characteristic motivic cohomology
本文证明混合特征概形的母题上同调满足Weibel消没的母题精细化、射影丛公式等预期性质，并将其与Milnor K理论比较，从而把Elmanto–Morrow的结果推广到非域上概形。
A smooth projective scheme $X$ over a field $k$ is said to satisfy the Rost nilpotence principle if any endomorphism of $X$ in the category of Chow motives that vanishes on an extension of the base field $k$ is nilpotent. We show that an étale motivic analogue of the Rost nilpotence principle holds for all smooth projective schemes over a perfect field. This provides a new approach to the question of Rost nilpotence and allows us to obtain an elegant proof of Rost nilpotence for surfaces, as well as for birationally ruled threefolds over a field of characteristic $0$.
On motivic cohomology of commutative C*-algebras
本文对紧Hausdorff空间上连续函数环的Cortiñas--Thom结果进行动机细化，证明其整动机上同调与Betti上同调的自然同构。
This note addresses the motivic nature of some classical cohomological results due to Lefschetz, namely the primitive decomposition (for the cohomology of smooth projective varieties), and, secondly, the splitting of the cohomology of a complete intersection into the "fixed" and "variable part".
We present a formal scheme based cycle model for the motivic cohomology of the fat points defined by the truncated polynomial rings $k[t]/(t^m)$ with $m \geq 2$, in one variable over a field $k$. We compute their Milnor range cycle class groups when the field has sufficiently many elements. With some aids from rigid analytic geometry and the Gersten conjecture for the Milnor $K$-theory resolved by M. Kerz, we prove that the resulting cycle class groups are isomorphic to the Milnor $K$-groups of the truncated polynomial rings, generalizing a theorem of Nesterenko-Suslin and Totaro.
Motivic cohomology of equicharacteristic schemes
本文构建了等特征方案的motivic cohomology理论，关联到非连通代数K-理论及etale上同调，并在光滑变元上恢复经典motivic cohomology。
Beilinson--Lichtenbaum phenomenon for motivic cohomology
研究非\(\mathbb{A}^1\)不变动机上同调，通过证明\(p\)进动机上同调到巴特 - 卢里合系上同调的圈类映射是同构，验证猜想，还证明了能恢复经典定义及给出纯度定理，关键是加伯表示引理的混合特征非诺特版本。
Arakelov motivic cohomology I
本文给出了算术环上有限型格式的一个新的上同调理论。这个动机上同调的Arakelov理论版本的主要动机是由第二作者提出的关于$L$ -函数和zeta函数的特殊值的猜想。利用motivic稳定同伦理论中的六函子形式，我们建立了一些形式性质，包括任意态射的拉回，正则概型之间的射影态射的前推，局部化序列，$h$ -下降.我们舍入图片与纯度的结果和更高的算术Riemann-Roch定理。
On 2-torsion in motivic cohomology
本文证明了Tosion上的Beilinson-Lichtenbaum图在动机上同调下的2-局部部分。特别是我们证明了Milnor猜想有关Milnor的K-理论和伽罗瓦上同调与Z/2-系数。这篇论文是以前发行的预印本“米尔诺猜想”的新版本。
We perform Hochschild homology calculations in the algebro-geometric setting of motives. The motivic Hochschild homology coefficient ring contains torsion classes which arise from the mod-$p$ motivic Steenrod algebra and from generating functions on the natural numbers with finite non-empty support. Under the Betti realization, we recover Bökstedt's calculation of the topological Hochschild homology of finite prime fields.
Milnor-Witt motivic cohomology of complements of hyperplane arrangements
本文计算仿射空间中超平面排列补集的Milnor-Witt动机上同调，给出其代数结构，并通过实现到经典上同调获得推论。
Towards motivic quantum cohomology of $\bar{M}_{0,S}$
我们显式地计算了亏格为零的标号曲线到亏格为零的标号曲线的模空间的映射所决定的Gromov-Witten对应。我们认为这些计算是研究动机量子上同调的自指性质的第一步。
From algebraic cobordism to motivic cohomology
设S是特征指数为c的域上的本质光滑概形。设MGL和HZ分别表示S上的代数配边谱和动机上同调谱。我们证明了典范映射MGL/（a1，a2，.）->由动机上同调的加性方向诱导的HZ在将c倒置后成为等价的。作为应用，我们证明了Atiyah-Hirzebruch谱序列对所有Z[1/c]-局部Landweber精确运动谱的收敛性.
We present a version of projective bundle theorem in MW-motives (resp. Chow-Witt rings), which says that $\widetilde{CH}^*(\mathbb{P}(E))$ is determined by $\widetilde{CH}^*(X)$, $\widetilde{CH}^*(X,det(E)^{\vee})$, $CH^*(X)$ and $Sq^2$ for smooth quasi-projective schemes $X$ and vector bundles $E$ over $X$ with $e(E^{\vee})=0\in H^n(X,W(det(E)))$, provided that $_2CH^*(X)=0$. As an application, we compute the MW-motives of blow-ups with smooth centers. Moreover, we discuss the invariance of Chow-Witt cycles of projective bundles under automorphisms of vector bundles.
Motivic cohomology of cyclic coverings
本文研究了循环覆盖的motivic cohomology，证明在特定情况下，循环覆盖的chow群在张量有理数后或不张量时均变得平凡。
Algebraic part of motivic cohomology with compact supports
本文将代数等价关系与正则同态推广至域上Voevodsky motives，证明了特定上同调群存在泛正则同态，恢复Murre定理等经典结论，并涵盖高阶Chow群与Milnor K-群。
For $k$ a perfect field of characteristic $p>0$ and $G/k$ a split reductive group with $p$ a non-torsion prime for $G,$ we compute the mod $p$ motivic cohomology of the geometric classifying space $BG_{(r)}$, where $G_{(r)}$ is the $r$th Frobenius kernel of $G.$ Our main tool is a motivic version of the Eilenberg-Moore spectral sequence, due to Krishna. For a flat affine group scheme $G/k$ of finite type, we define a cycle class map from the mod $p$ motivic cohomology of the classifying space $BG$ to the mod $p$ étale motivic cohomology of the classifying stack $\mathcal{B}G.$ This also gives …
We prove a mixed characteristic analog of the Beilinson-Lichtenbaum Conjecture for p-adic motivic cohomology. It gives a description, in the stable range, of p-adic motivic cohomology (defined using algebraic cycles) in terms of differential forms. This generalizes a result of Geisser from small Tate twists to all twists and uses as a critical new ingredient the comparison theorem between syntomic complexes and p-adic nearby cycles proved recently in Colmez-Niziol.
Combining work of Peyre, Colliot-Thélène and Voisin, we give the first example of a finite group $G$ such that the motivic class of its classifying stack $BG$ in Ekedahl's Grothendieck ring of stacks over $\mathbb{C}$ is non-trivial and $BG$ has trivial unramified Brauer group.
Lectures on motivic cohomology 2000/2001 (written by Pierre Deligne)
这些课堂讲稿涵盖四个主题。证明了在motivic同伦范畴上的motivic Eilenberg-Maclane空间所表示的函子与motivic复形所定义的motivic上同调是一致的。给出了有限平坦群概型（在Noether基上）的等变动机同伦范畴的描述以及A^1-等价的新刻画。有一部分我们介绍了一类层，叫做固体层。最后有一部分我们研究了形式为X -> X/G和X -> X^W的函子，并证明了它们保持了项式ind-solid单纯层之间的等价性。
Revisiting Dwork cohomology: Visibility and divisibility of Frobenius eigenvalues in rigid cohomology
该研究通过Dwork方法探究有限域上代数簇紧支集刚性上同调的Frobenius特征值，得到两个算术推论：仿射簇zeta函数可见证相关特征值，且刚性上同调的q-可除性下界优于ℓ进上同调的已知结果。
The realization of the degree zero part of the motivic polylogarithm on abelian schemes in Deligne-Beilinson cohomology
我们使用Burgos理论的算术周群展示的实现度零部分的多对数的交换计划在Deligne-Beilinson上同调。
Motivic p-adic tame cohomology
本文构造了正特征域上tame motives与log-étale motives间的比较函子，推广了已有拓扑比较，并构建了表示模$p^m$ tame motivic cohomology的$E_\infty$-环谱，证明了相关猜想。
Milnor-Witt motivic cohomology and linear algebraic groups
本文计算了辛群及一般线性群等线性代数群的 Milnor-Witt 动机上同调，并确定了其乘法结构。
Hermitian $K$-theory and Milnor-Witt motivic cohomology over $\mathbb Z$
本文利用Milnor-Witt母题上同调与切片谱序列计算Hermitian $K$-群，证明Grothendieck-Riemann-Roch定理，并给出整数环的Hermitian $K$-群与高阶Witt群。
Motivically functorial coniveau spectral sequences; direct summands of cohomology of function fields
我们构建了一个“三角模拟"coniveau谱序列：主题的各种可数字段是”分解“（在这个意义上的Postnikov塔）到扭曲（共）动机的点，这是广义任意Voevodsky的动机。为此，我们构建了一个'Gersten'的重量结构的一定的三角范畴的'comotives'：后者被定义为包含comotives的所有投射极限的光滑簇的重量结构的定义在前面的文件中介绍。相应的权重谱序列本质上是coniveau 1;它们是$DM^{eff}_{gm}$ -函子（从$E_2$开始），并且可以根据类别$DM^-_{eff}$的同伦$t$ -结构来计算（类似于光滑簇的情况）。这就把Bloch和Ogus开创性的coniveau谱序列计算扩展到动机上。我们还得到了一个光滑的半局部计划的上同调是一个直接和的上同调的一般纤维;上同调的函数域包含扭曲的上同调的剩余域（所有的几何赋值）。我们还进一步发展的一般理论的重量结构的三角范畴（独立于“动机”的一部分文件）。此外，我们还发展了一个关于三角范畴的“好”配对的理论，这似乎是一个新的课题。
Motivic homotopy theory with ramification filtrations
本文推广Morel–Voevodsky动机同伦理论，发展了带分歧滤子的同伦理论，刻画野生分歧等非𝔸¹同伦不变现象，证明相关上同调理论可在该范畴中表示并恢复已知构造。
We prove equivariant versions of the Beilinson-Lichtenbaum conjecture for Bredon motivic cohomology of smooth complex and real varieties with an action of the group of order two. This identifies equivariant motivic and topological invariants in a large range of degrees.
We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit description of these quantities we can answer in part to questions concerning the motivic nearby cycles of restriction functions and the integral identity conjecture in the context of Newton nondegenerate polynomials. Furthermore, in the nondegeneracy in the sense of Kouchnirenko, we give calculations on cohomology groups of the contact loci.
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。