Research on algebraic cycles on arithmetic schemes

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We study arithmetic properties, including finiteness, of the Chow group of 1-cycles on arithmetic schemes, especially regular semistable families on p-adic integer rings. The main tool in in this approach is the cycle class map to the etale cohomology. We derive properties of cycles by showing the injectivity and surjectivity of this cycle class map. In fact, we obtained a stong l-adic property of the 1-cycles in some quite general situation, and were able to compute the Chow group of 0-cycles on some special rational surface over a p-adic field.