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Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories /
The authors develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. They resolve the longstanding confusion about localization sequences in THH and TC, and establish a specialized dévissage theorem. As applications, the authors pro...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
[2020].
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1286. |
| Temas: |
$K$-theory [See also 16E20, 18F25]
> Higher algebraic $K$-theory
> $K$-theory and homology; cyclic homology and cohomology [See also 18G60].
Algebraic topology
> Homotopy theory {For simple homotopy type, see 57Q10}
> Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.).
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| Acceso en línea: | Texto completo |
MARC
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|---|---|---|---|
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| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 019 | |a 1159460285 | ||
| 020 | |a 1470461404 |q ebook | ||
| 020 | |a 9781470461409 |q ebook | ||
| 020 | |z 1470441780 | ||
| 020 | |z 9781470441784 | ||
| 029 | 1 | |a AU@ |b 000069393666 | |
| 035 | |a (OCoLC)1159163192 |z (OCoLC)1159460285 | ||
| 050 | 4 | |a QA612.33 |b .B56 2020eb | |
| 082 | 0 | 4 | |a 512/.66 |2 23 |
| 084 | |a 19D55 |a 55P43 |a 19L41 |a 19D10 |2 msc | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Blumberg, Andrew J., |e author. | |
| 245 | 1 | 0 | |a Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories / |c Andrew J. Blumberg, Michael A. Mandell. |
| 264 | 1 | |a Providence : |b American Mathematical Society, |c [2020]. | |
| 264 | 4 | |c ©2020 | |
| 300 | |a 1 online resource (v, 112 pages) | ||
| 334 | |a single unit |2 rdami | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |2 rdaft | ||
| 353 | |a index |b index | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v no. 1286 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Description based upon print version of record. | |
| 505 | 0 | |a Cover -- Title page -- Introduction -- Chapter 1. Review of , , and -- 1.1. Review of spectral categories -- 1.2. Review of the construction of , , and -- 1.3. Review of the invariance properties of -- 1.4. The Dennis-Waldhausen Morita Argument -- Chapter 2. and of simplicially enriched Waldhausen categories -- 2.1. Simplicially enriched Waldhausen categories -- 2.2. Spectral categories associated to simplicially enriched Waldhausen categories -- 2.3. The \Sdot and Moore nerve constructions -- 2.4. The Moore \Spdot construction -- | |
| 505 | 8 | |a 2.5. , , and the cyclotomic trace -- Chapter 3. -theory theorems in and -- 3.1. The Additivity Theorem -- 3.2. The Cofiber Theorem -- 3.3. The Localization Theorem -- 3.4. The Sphere Theorem -- 3.5. Proof of the Sphere Theorem -- Chapter 4. Localization sequences for and -- 4.1. The localization sequence for of a discrete valuation ring -- 4.2. The localization sequence for ( ) and related ring spectra -- 4.3. Proof of the Dévissage Theorem -- Chapter 5. Generalization to Waldhausen categories with factorization -- 5.1. Weakly exact functors -- | |
| 505 | 8 | |a 5.2. Embedding in simplicially tensored Waldhausen categories -- 5.3. Spectral categories and Waldhausen categories -- Bibliography -- Index -- Back Cover. | |
| 520 | |a The authors develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. They resolve the longstanding confusion about localization sequences in THH and TC, and establish a specialized dévissage theorem. As applications, the authors prove conjectures of Hesselholt and Ausoni-Rognes about localization cofiber sequences surrounding THH(ku), and more generally establish a framework for advancing the Rognes program for studying Waldhausen's chromatic filtration on A(*). | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a K-theory. | |
| 650 | 0 | |a Algebraic topology. | |
| 650 | 0 | |a Cobordism theory. | |
| 650 | 0 | |a Homology theory. | |
| 650 | 6 | |a K-théorie. | |
| 650 | 6 | |a Topologie algébrique. | |
| 650 | 6 | |a Théorie des cobordismes. | |
| 650 | 6 | |a Homologie. | |
| 650 | 7 | |a Topología algebraica |2 embne | |
| 650 | 0 | 7 | |a Homología, Teoría de |2 embucm |
| 650 | 0 | 7 | |a Cobordismo, Teoría de |2 embucm |
| 650 | 7 | |a Algebraic topology |2 fast | |
| 650 | 7 | |a Cobordism theory |2 fast | |
| 650 | 7 | |a Homology theory |2 fast | |
| 650 | 7 | |a K-theory |2 fast | |
| 650 | 7 | |a $K$-theory [See also 16E20, 18F25] -- Higher algebraic $K$-theory -- $K$-theory and homology; cyclic homology and cohomology [See also 18G60]. |2 msc | |
| 650 | 7 | |a Algebraic topology -- Homotopy theory {For simple homotopy type, see 57Q10} -- Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.). |2 msc | |
| 650 | 7 | |a $K$-theory [See also 16E20, 18F25] -- Topological $K$-theory [See also 55N15, 55R50, 55S25] -- Connective $K$-theory, cobordism [See also 55N22]. |2 msc | |
| 650 | 7 | |a $K$-theory [See also 16E20, 18F25] -- Higher algebraic $K$-theory -- Algebraic $K$-theory of spaces. |2 msc | |
| 700 | 1 | |a Mandell, Michael A., |e author. | |
| 776 | 0 | 8 | |i Print version: |a Blumberg, Andrew J. |t Localization for THH(ku) and the Topological Hochschild and Cyclic Homology of Waldhausen Categories |d Providence : American Mathematical Society,c2020 |z 9781470441784 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1286. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6229929 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH38606884 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6229929 | ||
| 938 | |a YBP Library Services |b YANK |n 301341937 | ||
| 938 | |a EBSCOhost |b EBSC |n 2504087 | ||
| 994 | |a 92 |b IZTAP | ||