Iwasawa theory is basically the study of various modules over a commutative ring. It is a topic in algebraic number theory because the ring and the various modules that are studied arise in an arithmetic way. In classical Iwasawa theory, they arise in trying to understand the structure of certain Galois groups. One fixes a prime p. The ring is typically a formal power series ring in a finite number of variables over Zp, the ring of p-adic integers. It is a Domain. In fact, it is a Unique Factorization Domain. Some of the interesting modules that are studied are finitely generated torsion modules. Let X be such a module. Thus, there will a nonzero element f in which annihilates X. If there exist two nonzero annihilators of X in which are relatively prime, then one says that X is a pseudo-null module. One finds this terminology in Bourbaki. The purpose of this talk is to discuss examples of modules X occurring naturally in Iwasawa theory which are, or at least should be, pseudo-null and, in the opposite direction, modules X which are not pseudo-null and, even more strongly, have no nonzero submodules which are pseudo-null.
Donnerstag, den 24. Oktober 2019 um 17.15 Uhr, in INF 205, HS Mathematikon Donnerstag, den 24. Oktober 2019 at 17.15, in INF 205, HS Mathematikon
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Otmar Venjakob