In this article, we study several problems related to virtual traces for finite group actions on schemes of type over an algebraically closed field. We also discuss applications fixed-point sets. Our results generalize previous obtained by Deligne, Laumon, Serre, and others.

Research Article| September 01, 2014 Geochemistry Insights on the Genesis of Subduction-Related Heishan Magmatic Ni-Cu-(PGE) Deposit, Gansu, Northwestern China, at Southern Margin Central Asian Orogenic Belt* Wei Xie; Xie 1State Key Laboratory Ore Deposit Geochemistry, Institute Chinese Academy Sciences, 46th Guanshui Road, Guiyang, 550002, P. R. China Search for other works by this author on: GSW Google Scholar Xie-Yan Song; Song † †Corresponding author: e-mail, songxieyan@vip.gyig.ac.cn...

We prove that Frobenius eigenvalues of $\ell$-adic cohomology and intersection rigid spaces over $p$-adic local fields are algebraic integers we give bounds for their valuations. As an application, deduce weights, proving conjectures Bhatt, Hansen, Zavyalov. also examples monodromy-pure perverse sheaves on projective curves with non cohomology, answering a question Hansen

In this article, we develop a theory of Grothendieck's six operations for derived categories in \'etale cohomology Artin stacks. We prove several desired properties the operations, including base change theorem categories. This extends all previous theories on subject, recent one developed by Laszlo and Olsson, which are subject to more assumptions isomorphism is only constructed level sheaves. Moreover, our works higher stacks as well. Our method differs from approaches, exploit stable...

This paper studies the sliced nearby cycle functor and its commutation with duality. Over a Henselian discrete valuation ring, we show that this holds, confirming prediction of Deligne. As an application give new proof Beilinson's theorem vanishing commutes duality up to twist. excellent base scheme, modification base. We deduce preserves universal local acyclicity over regular also present Gabber's implies Noetherian

In this sequel of arXiv:1211.5294 and arXiv:1211.5948, we develop an adic formalism for \'etale cohomology Artin stacks prove several desired properties including the base change theorem. addition, define perverse t-structures on general perversity, extending Gabber's work schemes. Our results generalize Laszlo Olsson middle perversity. We continue to in world $\infty$-categories sense Lurie, by enhancing all derived categories, functors, natural transformations level $\infty$-categories.

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding="application/x-tex">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be an algebraically closed field. alttext="normal upper Lamda"> <mml:mi mathvariant="normal">Λ<!-- Λ --></mml:mi> encoding="application/x-tex">\Lambda</mml:annotation> a noetherian commutative ring annihilated by integer invertible...

Gabber a déduit son théorème d’indépendance de l la cohomologie d’intersection d’un résultat général stabilité sur les corps finis. Dans cet article, nous démontrons un analogue locaux ce général. Plus précisément, introduisons une notion pour systèmes complexes faisceaux l-adiques schémas type fini local équivariants sous des groupes finis et établissons sa par six opérations Grothendieck le foncteur cycles proches. Notre méthode permet d’obtenir nouvelle démonstration du Gabber. Nous...

We study the behavior of integral l-adic sheaves on schemes finite type over a local field under six operations and nearby cycle functor.

In this article, we develop a general technique for gluing subcategories of $\infty$-categories. We obtain categorical equivalences between simplicial sets associated to certain multisimplicial sets. Such can be used construct functors in different contexts. One our results generalizes Deligne's theory developed the construction extraordinary pushforward operation \'etale cohomology schemes. Our are applied subsequent articles Grothendieck's six operations Artin stacks.

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Abstract We prove a relative Lefschetz–Verdier theorem for locally acyclic objects over Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$ -category of cohomological correspondences. show that local acyclicity equivalent to dualisability deduce duality preserves acyclicity. As another application category correspondences, we nearby cycle functor Henselian valuation ring duals, generalising Gabber.

Abstract Let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>𝐅</m:mi> <m:mi>q</m:mi> </m:msub> </m:math> \mathbf{F}_{q} be a finite field of q elements. For multiplicative characters <m:mrow> <m:mi>χ</m:mi> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mi>…</m:mi> <m:mi>m</m:mi> </m:mrow> \chi_{1},\ldots,\chi_{m} <m:msubsup> <m:mo>×</m:mo> </m:msubsup> \mathbf{F}_{q}^{\times} , we let <m:mi>J</m:mi> <m:mo>⁢</m:mo> <m:mo>(</m:mo> <m:mo>)</m:mo> J(\chi_{1},\ldots,\chi_{m}) denote the...

We show that compatible systems of $\ell$-adic sheaves on a scheme finite type over the ring integers local field are along boundary up to stratification. This extends theorem Deligne curves field. As an application, we deduce equicharacteristic case classical conjectures $\ell$-independence for proper smooth varieties complete discrete valuation fields. Moreover, have ramification. also prove analogue integrality boundary.

Gabber deduced his theorem of independence $l$ intersection cohomology from a general stability result over finite fields. In this article, we prove an analogue local More precisely, introduce notion for systems complexes $l$-adic sheaves on schemes type field, equivariant under groups. We establish its by Grothendieck's six operations and the nearby cycle functor. Our method leads to new proof Gabber's theorem. also give generalization algebraic stacks. ----- d\'eduit son th\'eor\`eme...

We present Gabber's theorem of independence $l$ for the intersection cohomology a proper equidimensional scheme over spectrum finite field. follow [Fuji] very closely. ----- On expose ici le théorème de Gabber d'indépendance pour la cohomologie d'intersection d'un schéma propre équidimensionnel sur spectre corps fini. suit à très peu près.

We prove a relative Lefschetz-Verdier theorem for locally acyclic objects over Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$-category of cohomological correspondences. show that local acyclicity equivalent to dualizability deduce duality preserves acyclicity. As another application category correspondences, we nearby cycle functor Henselian valuation ring duals, generalizing Gabber.