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Rationality problem for Algebraic Tori / Akinari Hoshi, Aiichi Yamasaki

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Hoshi, Akinari, 1978- [VerfasserIn]

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Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Memoirs of the American Mathematical Society ; volume 248, number 1176Verlag: Providence, Rhode Island : American Mathematical Society, 2017Beschreibung: 1 Online-Ressource (v, 215 pages)Schlagwörter:

Andere physische Formen: 1470424096 | 9781470424091 | 1470440547. | 9781470440541. | Erscheint auch als: Kein Titel Druck-Ausgabe | Print version: Kein Titel MSC: MSC: *11E72 | 12F20 | 13A50 | 14E08 | 20C10 | 20G15LOC-Klassifikation:

QA176

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Zusammenfassung: The authors give the complete stably rational classification of algebraic tori of dimensions 4 and 5 over a field k. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank 4 and 5 is given. The authors show that there exist exactly 487 (resp. 7, resp. 216) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 4, and there exist exactly 3051 (resp. 25, resp. 3003) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 5. The authors mZusammenfassung: Cover; Title page; Chapter 1. Introduction; Chapter 2. Preliminaries: Tate cohomology and flabby resolutions; Chapter 3. CARAT ID of the ℤ-classes in dimensions 5 and 6; Chapter 4. Krull-Schmidt theorem fails for dimension 5; 4.0. Classification of indecomposable maximal finite groups ≤\GL( ,\bZ) of dimension ≤6; 4.1. Krull-Schmidt theorem (1); 4.2. Krull-Schmidt theorem (2); 4.3. Maximal finite groups ≤\GL( ,\bZ) of dimension ≤6; 4.4. Bravais groups and corresponding quadratic forms; Chapter 5. GAP algorithms: the flabby class [ _{ }]^{ }Zusammenfassung: Cover; Title page; Chapter 1. Introduction; Chapter 2. Preliminaries: Tate cohomology and flabby resolutions; Chapter 3. CARAT ID of the ℤ-classes in dimensions 5 and 6; Chapter 4. Krull-Schmidt theorem fails for dimension 5; 4.0. Classification of indecomposable maximal finite groups ≤\GL( ,\bZ) of dimension ≤6; 4.1. Krull-Schmidt theorem (1); 4.2. Krull-Schmidt theorem (2); 4.3. Maximal finite groups ≤\GL( ,\bZ) of dimension ≤6; 4.4. Bravais groups and corresponding quadratic forms; Chapter 5. GAP algorithms: the flabby class [ _{ }]^{ }Zusammenfassung: The authors give the complete stably rational classification of algebraic tori of dimensions 4 and 5 over a field k. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank 4 and 5 is given. The authors show that there exist exactly 487 (resp. 7, resp. 216) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 4, and there exist exactly 3051 (resp. 25, resp. 3003) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 5. The authors mPPN: PPN: 1003033075Package identifier: Produktsigel: ZDB-4-NLEBK

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