A spectral sequence for Iwasawa adjoints

We establish a purely algebraic tool for studying the Iwasawa adjoints of some natural Iwasawa modules for $p$-adic Lie group extensions of number fields, by relating them to certain continuous Galois cohomology groups via a spectral sequence.Comment: 16 pages, 7 figure

Kato conjecture and motivic cohomology over finite fields

For an arithmetical scheme X, K. Kato introduced a certain complex of Gersten-Bloch-Ogus type whose component in degree a involves Galois cohomology groups of the residue fields of all the points of X of dimension a. He stated a conjecture on its homology generalizing the fundamental exact sequences for Brauer groups of global fields. We prove the conjecture over a finite field assuming resolution of singularities. Thanks to a recently established result on resolution of singularities for embedded surfaces, it implies the unconditional vanishing of the homology up to degree 4 for X projective smooth over a finite field. We give an application to finiteness questions for some motivic cohomology groups over finite fields.Comment: 38 page

Smooth representations and sheaves

The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we calculate the cohomology groups of several classes of smooth representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of an algebraically closed field.Comment: 20 pages, final versio

Do we face a credit crunch?.

The weakness of credit growth in the United States and Europe has given rise to concerns that the financial crisis has led to a credit crunch which has deepened the recession in the real economy and poses a serious threat to the recovery that seems to have started in the most recent months. In this contribution we find that so far the development of credit aggregates and interest rates for loans does not provide strong evidence for a supply restraint that goes beyond hat could be expected given the deterioration of the quality of borrowers against the background of the exceptionally severe economic downturn. Still, the behaviour of interest rate spreads in the United States does indicate that the effectiveness of monetary policy is reduced for the time being as a result of distress in the financial sector, and we see some risks that inappropriate bank capitalization may restrain credit growth and threaten the current recovery, especially in Germany where core capital is low by international standards. Policy measures to avoid a credit crunch should focus on preventing undercapitalization of banks from becoming a serious limitation to credit growth.Kreditmarkt; Kreditrationierung; Zinsstruktur; Bankenpolitik; Eigenkapital; Deutschland;