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Relevant bibliographies by topics / Algebraic schemes, cohomology theory, algebraic cycles, homotopy theory

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Academic literature on the topic 'Algebraic schemes, cohomology theory, algebraic cycles, homotopy theory'

Author: Grafiati

Published: 9 March 2023

Last updated: 19 July 2025

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Journal articles on the topic "Algebraic schemes, cohomology theory, algebraic cycles, homotopy theory"

1

Schreieder, Stefan. "Refined unramified cohomology of schemes." Compositio Mathematica 159, no. 7 (2023): 1466–530. http://dx.doi.org/10.1112/s0010437x23007236.

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We introduce the notion of refined unramified cohomology of algebraic schemes and prove comparison theorems that identify some of these groups with cycle groups. This generalizes to cycles of arbitrary codimension previous results of Bloch–Ogus, Colliot-Thélène–Voisin, Kahn, Voisin, and Ma. We combine our approach with the Bloch–Kato conjecture, proven by Voevodsky, to show that on a smooth complex projective variety, any homologically trivial torsion cycle with trivial Abel–Jacobi invariant has coniveau $1$ . This establishes a torsion version of a conjecture of Jannsen originally formulated

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2

Lesch, Matthias, Henri Moscovici, and Markus J. Pflaum. "Relative pairing in cyclic cohomology and divisor flows." Journal of K-Theory 3, no. 2 (2008): 359–407. http://dx.doi.org/10.1017/is008001021jkt051.

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AbstractWe construct invariants of relative K-theory classes of multiparameter dependent pseudodifferential operators, which recover and generalize Melrose's divisor flow and its higher odd-dimensional versions of Lesch and Pflaum. These higher divisor flows are obtained by means of pairing the relative K-theory modulo the symbols with the cyclic cohomological characters of relative cycles constructed out of the regularized operator trace together with its symbolic boundary. Besides giving a clear and conceptual explanation to the essential features of the divisor flows, namely homotopy invari

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3

Toën, Bertrand, and Gabriele Vezzosi. "Algèbres simplicialesS1-équivariantes, théorie de de Rham et théorèmes HKR multiplicatifs." Compositio Mathematica 147, no. 6 (2011): 1979–2000. http://dx.doi.org/10.1112/s0010437x11005501.

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AbstractThis work establishes a comparison between functions on derived loop spaces (Toën and Vezzosi,Chern character, loop spaces and derived algebraic geometry, inAlgebraic topology: the Abel symposium 2007, Abel Symposia, vol. 4, eds N. Baas, E. M. Friedlander, B. Jahren and P. A. Østvær (Springer, 2009), ISBN:978-3-642-01199-3) and de Rham theory. IfAis a smooth commutativek-algebra andkhas characteristic 0, we show that two objects,S1⊗Aand ϵ(A), determine one another, functorially inA. The objectS1⊗Ais theS1-equivariant simplicialk-algebra obtained by tensoringAby the simplicial groupS1:=

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4

Beraldo, Dario, та Massimo Pippi. "Non-commutative nature of ℓ-adic vanishing cycles". Journal für die reine und angewandte Mathematik (Crelles Journal), 23 січня 2025. https://doi.org/10.1515/crelle-2024-0099.

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Abstract Let p : X → S p\colon X\to S be a flat (proper) and regular scheme of finite type over a strictly henselian discrete valuation ring. We prove that the singularity category of the special fiber with its natural two-periodic structure allows to recover the ℓ-adic vanishing cohomology of 𝑝. Along the way, we compute homotopy-invariant non-connective algebraic K-theory with compact support of certain embeddings X t ↪ X T X_{t}\hookrightarrow X_{T} in terms of the motivic realization of the dg-category of relatively perfect complexes.

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BACHMANN, Tom, and Marc HOYOIS. "Norms in motivic homotopy theory." Astérisque 425 (September 1, 2021). http://dx.doi.org/10.24033/ast.1147.

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If $f : S' \to S$ is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor $f_\otimes : \mathcal{H}_{\bullet}(S')\to \mathcal{H}_{\bullet}(S)$, where $\mathcal{H}_\bullet(S)$ is the pointed unstable motivic homotopy category over $S$. If $f$ is finite étale, we show that it stabilizes to a functor $f_\otimes : \mathcal{S}\mathcal{H}(S') \to \mathcal{S}\mathcal{H}(S)$, where $\mathcal{S}\mathcal{H}(S)$ is the $\mathbb{P}^1$-stable motivic homotopy category over $S$. Using these norm functors, we define the notion of a normed motivic spectrum, which is an en

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Dissertations / Theses on the topic "Algebraic schemes, cohomology theory, algebraic cycles, homotopy theory"

1

BORGHESI, SIMONE. "Algebraic Morava K-theories and the higher degree formula." Doctoral thesis, Northwestern University, 2000. http://hdl.handle.net/10281/39205.

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This manuscript consists of two parts. In the first, a cohomology theory on the category of algebraic schemes over a field of characteristic zero is provided. This theory shares several properties with the topological Morava K-theories, hence the name. The second part contains a proof of Voevodsky and Rost conjectured degree formulae. The proof uses algebraic Morava K-theories.

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Books on the topic "Algebraic schemes, cohomology theory, algebraic cycles, homotopy theory"

1

Perfectoid Spaces: Lectures from the 2017 Arizona Winter School. American Mathematical Society, 2019.

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2

Kedlaya, Kiran S., Debargha Banerjee, Ehud de Shalit, and Chitrabhanu Chaudhuri. Perfectoid Spaces. Springer Singapore Pte. Limited, 2022.

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Perfectoid Spaces. Springer, 2023.

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Hilbert Schemes of Points and Infinite Dimensional Lie Algebras. American Mathematical Society, 2018.

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