Harari, D. and Szamuely, Tamás (2016) Localglobal questions for tori over padic function fields. JOURNAL OF ALGEBRAIC GEOMETRY, 25 (3). pp. 571605. ISSN 10563911

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Abstract
We study localglobal questions for Galois cohomology over the function field of a curve defined over a padic field (a field of cohomological dimension 3). We define TateShafarevich 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 TateShafarevich group of the torus and the second TateShafarevich group of the dual torus. Building upon the duality theorem, we show that the failure of the localglobal 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.
Item Type:  Article 

Uncontrolled Keywords:  Kernel; 1MOTIVES; COMPLEXES; cohomology; CURVES; DUALITY THEOREMS; HASSE PRINCIPLE; BLOCHKATO CONJECTURE; LINEAR ALGEBRAICGROUPS 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  03 Jan 2017 14:01 
Last Modified:  03 Jan 2017 14:02 
URI:  http://real.mtak.hu/id/eprint/44233 
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