The intersection homology D--module in finite characteristic
| dc.creator | Blickle, Manuel | |
| dc.date | 2001-10-22 | |
| dc.date.accessioned | 2026-07-07T04:44:01Z | |
| dc.date.available | 2026-07-07T04:44:01Z | |
| dc.description | Let R be a regular, local and F-finite ring defined over a field of finite characteristic. Let I be an ideal of height c with normal quotient $A=R/I$. It is shown that the local cohomology module H^c_I(R) contains a unique simple D_R--submodule L(A,R). This should be viewed as a finite characteristic analog of the Kashiwara--Brylinski D_R--module in characteristic zero which corresponds to the intersection cohomology complex via the Riemann--Hilbert correspondence. Besides the existence of L(A,R), more importantly, we give its construction as a certain dual of the tight closure of zero in $H^d_m(A)$. We obtain a precise D_R--simplicity criterion for H^c_I(R), namely H^c_I(R) is D_R--simple if and only if the tight closure of zero in H^d_m(A) is Frobenius nilpotent, in particular this is the case if A is F--rational. Furthermore, the techniques developed imply a result in tight closure theory, saying that the parameter test module commutes with completion. | |
| dc.description | University of Michigan Dissertation | |
| dc.identifier | https://arxiv.org/abs/math/0110244 | |
| dc.identifier | http://arxiv.org/abs/math/0110244 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62467 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14F43; 14B15; 13N10 | |
| dc.title | The intersection homology D--module in finite characteristic | |
| dc.type | text |