| This thesis studies the local cohomology modules over polynomial rings of prime characteristic.;Many great mathematicians have contributed to the theory of local cohomology. However, the structure of local cohomology modules is still full of mystery. In most cases HiI(M) is not finitely generated. So it is very difficult to tell whether the local cohomology modules are 0 or not, and it is also the main reason it had been a long time before an algorithm was found in characteristic 0 and implemented into computer programs.;We study the local cohomology modules of polynomial rings in prime characteristic. Let R be a polynomial ring over a field k of characteristic p>0. If I is an ideal of R, we denote Hi I(M) the i-th local cohomology module of R with support in I. After some introductory material on local cohomology, we will give a lower bound of the dimension of associated primes of HiI (M) in terms of the degrees of the generators of I. Let m be the maximal ideal generated by the variables and let I1,...,Is be homogeneous ideals of R. We will describe the grading of the composition of local cohomology at m, I 1,...,Is, and also give two algorithms to calculate it. |
