| Tartalom: |
http://real.mtak.hu/44233/ |
| Archívum: |
MTA Könyvtár |
| Gyűjtemény: |
Status = Published
Type = Article
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| Cím: |
Local-global questions for tori over p-adic function fields
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| Létrehozó: |
Harari, D.
Szamuely, Tamás
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| Kiadó: |
American Mathematical Society
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| Dátum: |
2016
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| Téma: |
QA Mathematics / matematika
QA72 Algebra / algebra
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| Tartalmi leírás: |
We study local-global questions for Galois cohomology over the function field of a curve defined over a p-adic field (a field of cohomological dimension 3). We define Tate-Shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of the base field coming from a closed point of the curve. In the case of a torus we establish a perfect duality between the first Tate-Shafarevich group of the torus and the second Tate-Shafarevich group of the dual torus. Building upon the duality theorem, we show that the failure of the local-global principle for rational points on principal homogeneous spaces under tori is controlled by a certain subquotient of a third etale cohomology group. We also prove a generalization to principal homogeneous spaces of certain reductive group schemes in the case when the base curve has good reduction.
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| Nyelv: |
angol
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| Típus: |
Article
PeerReviewed
info:eu-repo/semantics/article
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| Formátum: |
text
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| Azonosító: |
Harari, D. and Szamuely, Tamás (2016) Local-global questions for tori over p-adic function fields. JOURNAL OF ALGEBRAIC GEOMETRY, 25 (3). pp. 571-605. ISSN 1056-3911
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| Kapcsolat: |
MTMT:3155452; doi:10.1090/jag/661
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