Iwasawa Theory, projective modules, and modular representations

Galois modules, Iwasawa theory and leading term conjectures

ON PROJECTIVE L- MODULES

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

The Homotopy Theory of Projective Modules

Serre [8; 9] has established the rudiments of a dictionary for translating the language of projective modules into that of vector bundles. With this point of departure we have attempted to adapt some of the results and methods of homotopy theory to certain purely arithmetic and even noncommutative settings. Detailed proofs of our results will appear elsewhere. The authors are very grateful to A...

On two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective

Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...

Filtrations of smooth principal series and Iwasawa modules

Let $G$ be a reductive $p$-adic group‎. ‎We consider the general question‎ ‎of whether the reducibility of an induced representation can be detected in a‎ ‎``co-rank one‎" ‎situation‎. ‎For smooth complex representations induced from supercuspidal‎ ‎representations‎, ‎we show that a sufficient condition is the existence of a subquotient‎ ‎that does not appear as a subrepresentation‎. ‎An import...