JP Journal of Algebra, Number Theory and Applications
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Abstract: Letbe a prime
number andbe an
arbitrary finite Galois
-extension of function fields of one variable with field of constants k,
an algebraically closed field of characteristicIn the
wildly ramified case, i.e.,we obtain the Galois module
structure of the incomplete generalized Jacobian and of the elements of order dividing p
of associated with the modulus in L
which is induced by a modulus in K,
where not necessarily contains in its
support all the prime divisors of K
ramified in L. That is, we obtain
explicitly the decomposition of as direct sum of indecomposable
-modules For the tamely ramified case, i.e., when the modulus in K
contains in its support all except one
of the prime divisors of K ramified in
L, we obtain explicitly the decomposition of the
-part of as direct sum of indecomposable
-modules
Keywords and phrases: integral representation, Galois modules, Galois cohomology, injective modules, class groups, Jacobian, generalized Jacobian.
