In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly...In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.展开更多
Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they...Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they are compatible with Poincaréduality and with the canonical morphisms among such cohomology.We deduce these results from their analogues for rigid analytic varieties that are Zariski open in some proper smooth rigid analytic varieties over k.In particular,we prove finiteness ofétale cohomology with partial compact support of any Z_(p)-local systems,and establish the Poincaréduality for such cohomology after inverting p.展开更多
文摘In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.
文摘Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they are compatible with Poincaréduality and with the canonical morphisms among such cohomology.We deduce these results from their analogues for rigid analytic varieties that are Zariski open in some proper smooth rigid analytic varieties over k.In particular,we prove finiteness ofétale cohomology with partial compact support of any Z_(p)-local systems,and establish the Poincaréduality for such cohomology after inverting p.
