Boundary value problems and Index Theorem for D Modules
D 模的边值问题和指数定理
基本信息
- 批准号:16540150
- 负责人:
- 金额:$ 2.54万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2004
- 资助国家:日本
- 起止时间:2004 至 2007
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
We have found an idea to formulate elliptic boundary value problems for systems of differential equations in terms of D-Modules and to construct their characteristic cycles (or microlocal Euler classes). Let us consider a system of differential equations M on a manifold M with boundary N. Let M_<tan> denote its pull back to the boundary. Given a system of differential equations N on the boundary and a D_N linear morphism α: N → M_<tan>. By definition, this boundary value problem is said to be elliptic if a induces an isomorphism from ε_N [○!×] N to a coherent quotient module M^+(tan)of ε_N [○!×] M^<tan> defined microlocally from the boundary. (ε_N is the sheaf of rings of microdifferential operators on the boundary.) It is still difficult to construct a characteristic cycle in this naive setting, and we want to translate this setting of BVP as a module (or an object of a derived category of modules) over some ring. If we introduce the ring BD as BD = D_M [○!+] D(N,M) [○!+]D_N, we can get an object B (M, N) of the derived category D^b(D_M [○!×] B), with B the ring of upper half triangle matrices of degree 2. One can possibly define a characteristic cycle (or a microlocal Euler class) associated to the pair of a D_M [○!×]B-module and a B-module (Z_M, Z_N) by the diagonal argument under the condition of ellipticity of α. We expect that one can prove (by chasing diagrams) an index theorem for boundary value problems in terms of characteristic classes defined here, since their construction is almost totally functorial.
我们找到了一种用D-模表示微分方程组椭圆边值问题并构造其特征环(或微局部Euler类)的方法。让我们考虑一个微分方程组M在一个流形M上,边界N。让M_<tan>表示其拉回边界的拉力。给定一个边界上的微分方程组N和一个D_N线性态射α:N → M_<tan>。根据定义,如果a从ε_N [○!×] N到ε_N [○!从<tan>边界微局部地定义。(ε_N是微微分算子环在边界上的层。)在这个简单的设置中仍然很难构造一个特征循环,我们想把这个BVP设置转换为某个环上的一个模(或一个派生模范畴的对象)。如果我们引入环BD为BD = D_M [○!+] D(N,M)[○!+] D_N,我们可以得到导出范畴D^B(D_M [○!×] B),其中B是2次上半三角矩阵环。我们可以定义一个与D_M [○!×] B-模和一个B-模(Z_M,Z_N).我们期望可以证明(通过追逐图)的指标定理的边值问题的特征类定义在这里,因为他们的建设几乎完全是函。
项目成果
期刊论文数量(5)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
On the Cauchy problem for non effectively hyperbolic operatone, the Iurii-Petkou-Hormandes cond-ition and the Gevrey
关于非有效双曲运算的柯西问题、Iurii-Petkou-Hormandes条件和Gevrey
- DOI:
- 发表时间:2008
- 期刊:
- 影响因子:0
- 作者:Yamada;Yasutaka;S. Kanagawa;T. Nishitani
- 通讯作者:T. Nishitani
Second osdes weakly hyperbolic operators with coefficients sum of powers of functions
第二个 osdes 具有函数幂系数和的弱双曲算子
- DOI:
- 发表时间:2007
- 期刊:
- 影响因子:0
- 作者:竹中淑子;金川秀也;Tetsuo Ueda;Toshiaki Hishida;F. Colombini・T. Nishitani
- 通讯作者:F. Colombini・T. Nishitani
On the Cauchy problem for non effectively Puypertolic operatore, the Iwcu-Petkov-Hormanden condition and the Gevreg well poeedness
非有效 Puypertolic 算子的柯西问题、Iwcu-Petkov-Hormanden 条件和 Gevreg 井 Poeedness
- DOI:
- 发表时间:2008
- 期刊:
- 影响因子:0
- 作者:T.;Nishitani
- 通讯作者:Nishitani
An example of the Canchy problem well posed in any Geviey claee
任何 Geviey claee 中都能很好提出的 Canchy 问题的一个例子
- DOI:
- 发表时间:2007
- 期刊:
- 影响因子:0
- 作者:内藤敏機;申正善;F. Colombini・T. Nishitani
- 通讯作者:F. Colombini・T. Nishitani
An example of the Canchy Problem well pored in any Georey class
任何 Georey 课程中深入研究的 Canchy 问题的示例
- DOI:
- 发表时间:2007
- 期刊:
- 影响因子:0
- 作者:F.;Colombini;T.;Nishitani
- 通讯作者:Nishitani
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UCHIDA Motoo的其他文献
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{{ truncateString('UCHIDA Motoo', 18)}}的其他基金
Boundary Value Problems and Index Theorem for D-Modules
D 模的边值问题和指数定理
- 批准号:
12640172 - 财政年份:2000
- 资助金额:
$ 2.54万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
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