Jannsen, Uwe (2016) Hasse principles for higher-dimensional field. ANNALS OF MATHEMATICS, 183 (1). pp. 1-71. ISSN 0003-486X, 1939-8980
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For rather general excellent schemes X, K. Kato defined complexes of Gersten-Bloch-Ogus type involving the Galois cohomology groups of all residue fields of X. For arithmetically interesting schemes, he developed a fascinating web of conjectures on some of these complexes, which generalize the classical Hasse principle for Brauer groups over global fields, and proved these conjectures for low dimensions. We prove Kato's conjecture over number fields in any dimension. This gives a cohomological Hasse principle for function fields F over a number field K, involving the corresponding function fields F-v over the completions K-v of K. For global function fields K we prove the part on injectivity for coefficients invertible in K. Assuming resolution of singularities, we prove a similar conjecture of Kato over finite fields, and a generalization to arbitrary finitely generated fields.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MOTIVIC COHOMOLOGY; ALGEBRAIC VARIETY; NORM VARIETIES; FINITE-FIELDS; CHOW GROUP; K-THEORY; SINGULARITIES; CODIMENSION-2; RESOLUTION; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Uwe Jannsen |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Mar 2019 12:36 |
| Last Modified: | 07 Mar 2019 10:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2234 |
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