Yamazaki, Takao Tate duality and ramification of division algebras. (English) Zbl 1025.11036 Acta Math. Inform. Univ. Ostrav. 10, No. 1, 153-160 (2002). This is a survey paper without proofs. The author considers a ramification theory for division algebras with imperfect residue class field. He uses this theory for an application to the Tate duality for Jacobian varieties over finite extensions of \(\mathbb{Q}_p\). Reviewer: H.Koch (Berlin) MSC: 11S25 Galois cohomology 16K20 Finite-dimensional division rings 11S45 Algebras and orders, and their zeta functions Keywords:survey paper; ramification; division algebras; Tate duality; Jacobian varieties × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] Coates J., Greenberg R.: Kummer theory for abelian varieties over local fields. Invent. Math. 124, 129-174 (1996). · Zbl 0858.11032 · doi:10.1007/s002220050048 [2] Hyodo O.: Wild ramification in the imperfect residue field case. Adv. Stud. Pure Math., 12, 287-314 (1987). · Zbl 0649.12011 [3] Kato K.: A generalization of local class field theory by using K-groups. I. J. Fac. Sci. U. of Tokyo, Sec IA 26, 303-376 (1989). · Zbl 0428.12013 [4] Kato K.: Swan conductors for characters of degree one in the imperfect residue field case. Contemporary Math. 83, 101-131 (1989). · Zbl 0716.12006 · doi:10.1090/conm/083/991978 [5] McCallum W.: Tate duality and wild ramification. Math. Ann. 288, 553-558 (1990). · Zbl 0767.11057 · doi:10.1007/BF01444549 [6] Serre J.P.: Corps locaux. Hermann (1962). · Zbl 0137.02601 [7] Tate J.: WC-groups over p-adic fields. Seminaire Bourbaki, 156 13p (1957). · Zbl 0091.33701 [8] Yamazaki T.: Reduced norm map of division algebras over complete discrete valuation fields of certain type. Comp. Math. 112, 127-145 (1998). · Zbl 0990.11072 · doi:10.1023/A:1000439025718 [9] Yamazaki T.: On Swan conductors for Brauer groups of curves over local fields. Proc. Amer. Math. Soc. 127, 1269-1274 (1999). · Zbl 0921.14008 · doi:10.1090/S0002-9939-99-04775-9 [10] Yamazaki T.: On Tate duality for Jacobian varieties. preprint (2001). · Zbl 1049.11129 · doi:10.1016/S0022-314X(02)00067-7 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.