Demazure resolutions as varieties of lattices with infinitesimal structure

Let k be a field of positive characteristic. We construct, for each dominant coweight \lambda of the standard maximal torus in the special linear group, a closed subvariety D(\lambda) of the multigraded Hilbert scheme of an affine space over k, such that the k-valued points of D(\lambda) can be interpreted as lattices in k((z))^n endowed with infinitesimal structure. Moreover, for any \lambda we construct a universal homeomorphism from D(\lambda) to a Demazure resolution of the Schubert variety associated with \lambda in the affine Grassmannian. Lattices in D(\lambda) have non-trivial infinitesimal structure if and only if they lie over the boundary of the big cell.Comment: 24 pages, added the missing bibliograph

On p-adic lattices and Grassmannians

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of p-typical Witt vectors, k is a perfect field of characteristic p and G is a reductive group scheme over W(k). The present paper is an attempt to describe which constructions carry over from the function field case to the p-adic case, more precisely to the situation of the p-adic affine Grassmannian for the special linear group G=SL_n. We start with a description of the R-valued points of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R), where R is a perfect k-algebra. In order to obtain a link with geometry we further construct projective k-subvarieties of the multigraded Hilbert scheme which map equivariantly to the p-adic affine Grassmannian. The images of these morphisms play the role of Schubert varieties in the p-adic setting. Further, for any reduced k-algebra R these morphisms induce bijective maps between the sets of R-valued points of the respective open orbits in the multigraded Hilbert scheme and the corresponding Schubert cells of the p-adic affine Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math. Zeitschrift, of the previously published preprint "On p-adic loop groups and Grassmannians

Fiscal Implications of Population Ageing

The paper explores the long-term fiscal implications of population aging in the Czech Republic. The results, although bearing a significant margin of uncertainty due to the very long-term character of the projection exercise, do not impart encouraging fiscal outlooks for the Czech Republic. This is hardly surprising given that the Czech Republic is facing pronounced population ageing. Moreover, the fiscal position of the Czech Republic is presently very poor, in spite of its (still) low level of debt and debt interest payments. The Czech Republic?s high primary deficit will foster a rapid rise in debt irrespective of population ageing. Therefore, to cope with the expected fiscal pressures, it is necessary not only to overhaul the pension and health-care systems in the medium term, but also to immediately start an intensive strategy of consolidation aimed at significantly reducing the high primary deficit.ageing populations; fiscal policy; fiscal sustainability

Cyclically Adjusted Fiscal Balance: OECD and ESCB Methods

The paper considers the impact of the business cycle on Czech fiscal balance in the past decade. The authors employed two different calculation methods in their analysis: an OECD and an ESCB method. Two crucial findings emerged from the analysis. First, the estimates of cyclically adjusted deficits in the Czech Republic proved their robustness, because both our calculation methods, although being philosophically different, provided very similar results. Sharply deteriorating Czech budget deficits are basically structural in nature, i.e., they are independent of the business cycle. Moreover, another hypothesis was confirmed: Czech fiscal policy exhibits mainly pro-cyclical features. As the paper further documents, both basic assessments held true even when quasi-fiscal deficits were included in the analysis.off-budget transactions; quasi-fiscal policy; cyclically adjusted balance; fiscal stance; fiscal policy

Volga Bulgarian-Permic linguistic contact: Mutual influences on morphology

In this paper, I argue that three morphological (morphosyntactic) features in Udmurt, Komi, Volga Bulgarian and Chuvash show mutual influence between the Proto-Permic and Volga Bulgarian languages in the Volga-Kama area in the late first millennium CE: First, the formal identity of the Permic accusative and 3sg possessive suffixes which does not have parallels in Uralic but in Turkic. Second, the Volga Bulgarian and Chuvash plural marker -sem, which is unknown from other Turkic languages. Third, the prohibitive particle an in Chuvash, which does not have cognates in Turkic and is loaned from Proto-Permic