DOCUMENTA MATHEMATICA, Extra Volume: Kazuya Kato's Fiftieth Birthday (2003), 261-284

Ivan Fesenko

Analysis on Arithmetic Schemes. I

A shift invariant measure on a two dimensional local field, taking values in formal power series over reals, is introduced and discussed. Relevant elements of analysis, including analytic duality, are developed. As a two dimensional local generalization of the works of Tate and Iwasawa a local zeta integral on the topological Milnor $K_2^t$-group of the field is introduced and its properties are studied.

2000 Mathematics Subject Classification: 28B99, 28C99, 28E05, 28-99, 42-99, 11S99, 11M99, 11F99, 11-99, 19-99.

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