Learning the Umlaut

In September 2006, the Second Research Software Contest, held by the Online Computer Library Center (OCLC) awarded Ross Singer's Umlaut service, an OpenURL link resolver. The article investigates which of the Umlaut's services would be feasible in the SFX environment as well

Chai's conjecture for semiabelian Jacobians

We prove Chai's conjecture on the additivity of the base change conductor of semiabelian varieties in the case of Jacobians of proper curves. This includes the first infinite family of non-trivial wildly ramified examples. Along the way, we extend Raynaud's construction of the N\'eron lft-model of a Jacobian in terms of the Picard functor to arbitrary seminormal curves (beyond which Jacobians admit no N\'eron lft-models, as shown by our more general structural results). Finally, we investigate the structure of Jacobians of (not necessarily geometrically reduced) proper curves over fields of degree of imperfection at most one and prove two conjectures about the existence of N\'eron models and N\'eron lft-models due to Bosch-L\"utkebohmert-Raynaud for Jacobians of general proper curves in the case of perfect residue fields, thus strengthening the author's previous results in this situation.Comment: 35 page

SFX and DOI: How to make the best of it?

There are so many ways in which a link resolver can use the CrossRef/DOI framework, that even experienced SFX administrators may find it difficult to keep the overview as well as to select and configure the services appropriately. The poster will summarize the DOI experiences of the MPG/SFX admin team by describing selected usage scenarios (incl. "Metadata lookup", "Article level linking" and the "DOI cookie pusher"), and by discussing the benefits and consequences of each scenario

Degeneration of Kummer surfaces

We prove that a Kummer surface defined over a complete strictly Henselian discretely valued field K of residue characteristic different from 2 admits a strict Kulikov model after finite base change. The Kulikov models we construct will be schemes, so our results imply that the semistable reduction conjecture is true for Kummer surfaces in this setup, even in the category of schemes. Our construction of Kulikov models is closely related to an earlier construction of Künnemann, which produces semistable models of Abelian varieties. It is well known that the special fibre of a strict Kulikov model belongs to one of three types, and we shall prove that the type of the special fibre of a strict Kulikov model of a Kummer surface and the toric rank of a corresponding Abelian surface are determined by each other. We also study the relationship between this invariant and the Galois representation on the second ℓ-adic cohomology of the Kummer surface. Finally, we apply our results, together with earlier work of Halle–Nicaise, to give a proof of the monodromy conjecture for Kummer surfaces in equal characteristic zero

On Jacobians of geometrically reduced curves and their N\'eron models

We study the structure of Jacobians of geometrically reduced curves over arbitrary (i. e., not necessarily perfect) fields. We show that, while such a group scheme cannot in general be decomposed into an affine and an Abelian part as over perfect fields, several important structural results for these group schemes nevertheless have close analoga over non-perfect fields. We apply our results to prove two conjectures due to Bosch-L\"utkebohmert-Raynaud about the existence of N\'eron models and N\'eron lft-models over excellent Dedekind schemes in the special case of Jacobians of geometrically reduced curves. Finally, we prove some existence results for semi-factorial models and related objects for general geometrically integral curves in the local case.Comment: 49 Pages. Results unchanged. Several sections substantially rewritten and some proofs simplified. Typographical errors corrected, references adde