Study on arithmetic geometry by arithmetic cohomology

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In arithmetic geometry(=the conjunction of arithmetic andgeometry), there is a theory of p-adic cohomology. For this theory, we have constructed afundamental theory of logarithmic convergent topoi and proved various properties oflogarithmic weight filtration. We have also constructed the p-adic weight spectralsequences of proper varieties with any singularities over the fraction field of a completediscrete valuation ring of mixed characteristics and proved the fundamental properties ofit.