Hybrid journal (It can contain Open Access articles) ISSN (Print) 1073-7928 - ISSN (Online) 1687-0247 Published by Oxford University Press[406 journals]

Authors:Tang R; Webb R. Pages: 3301 - 3341 Abstract: We consider several natural sets of curves associated to a given Teichmüller disc, such as the systole set or cylinder set, and study their coarse geometry inside the curve graph. We prove that these sets are quasiconvex and agree up to uniformly bounded Hausdorff distance. We describe two operations on curves and show that they approximate nearest point projections to their respective targets. Our techniques can be used to prove a bounded geodesic image theorem for a natural map from the curve graph to the filling multi-arc graph associated to a Teichmüller disc. PubDate: Sat, 04 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw318 Issue No:Vol. 2018, No. 11 (2017)

Authors:Temkin M; Tyomkin I. Pages: 3342 - 3387 Abstract: In [17], the first author introduced (relative) Riemann–Zariski spaces corresponding to a morphism of schemes and established their basic properties. In this article, we clarify that theory and extend it to morphisms between algebraic spaces. As an application, a new proof of Nagata’s compactification theorem for algebraic spaces is obtained. PubDate: Mon, 06 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw339 Issue No:Vol. 2018, No. 11 (2017)

Authors:Cousin G; Moussard D. Pages: 3388 - 3442 Abstract: We give a complete description of finite braid group orbits in $\mathrm{Aff}(\mathbb{C})$-character varieties of the punctured Riemann sphere. This is performed, thanks to a coalescence procedure and to the theory of finite complex reflection groups. We then derive consequences in the theory of differential equations. These concern algebraicity of isomonodromic deformations for reducible rank two logarithmic connections on the sphere, the Riemann–Hilbert problem and $F_D$-type Lauricella hypergeometric functions.Ai nostri amici di Pisa. PubDate: Mon, 06 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw283 Issue No:Vol. 2018, No. 11 (2017)

Authors:Vezzani A. Pages: 3443 - 3489 Abstract: We construct the dagger realization functor for analytic motives over non-archimedean fields of mixed characteristic, as well as the Monsky–Washnitzer realization functor for algebraic motives over a discrete field of positive characteristic. In particular, the motivic language on the classic étale site provides a new direct definition of the overconvergent de Rham cohomology and rigid cohomology and shows that their finite dimensionality follows formally from one of Betti cohomology for smooth projective complex varieties. PubDate: Mon, 06 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw335 Issue No:Vol. 2018, No. 11 (2017)

Authors:Biswas I Mj M. Pages: 3490 - 3506 Abstract: We extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact Kähler manifolds to compact quasi-regular Sasakian manifolds. A particular consequence is the translation of restrictions on Kähler groups proved using the Donaldson-Corlette-Hitchin-Simpson correspondence to fundamental groups of compact Sasakian manifolds (not necessarily quasi-regular). PubDate: Mon, 20 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw329 Issue No:Vol. 2018, No. 11 (2017)

Authors:Bremer C; Sage D. Pages: 3507 - 3555 Abstract: The theory of minimal $K$-types for $p$-adic reductive groups was developed in part to classify irreducible admissible representations with wild ramification. An important observation was that minimal $K$-types associated to such representations correspond to fundamental strata. These latter objects are triples $(x, r, \beta)$, where $x$ is a point in the Bruhat-Tits building of the reductive group $G$, $r$ is a nonnegative real number, and $\beta$ is a semistable functional on the degree $r$ associated graded piece of the Moy–Prasad filtration corresponding to $x$.Recent work on the wild ramification case of the geometric Langlands conjectures suggests that fundamental strata also play a role in the geometric setting. In this paper, we develop a theory of minimal $K$-types for formal flat $G$-bundles. We show that any formal flat $G$-bundle contains a fundamental stratum; moreover, all such strata have the same rational depth. We thus obtain a new invariant of a flat $G$-bundle called the slope, generalizing the classical definition for flat vector bundles. The slope can also be realized as the minimum depth of a stratum contained in the flat $G$-bundle, and in the case of positive slope, all such minimal depth strata are fundamental. Finally, we show that a flat $G$-bundle is irregular singular if and only if it has positive slope. PubDate: Mon, 20 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw338 Issue No:Vol. 2018, No. 11 (2017)

Authors:Xu J. Pages: 3556 - 3586 Abstract: For the universal family of cyclic covers of projective spaces branched along hyperplane arrangements in general position, we consider its monodromy group acting on an eigenspace of the middle cohomology of the fiber. We prove the monodromy group is Zariski dense in the corresponding linear group. As an application, we show the fundamental group of the moduli space of hyperplane arrangements is large. It can be viewed as a degenerate analogy of Carlson-Toledo’s result about the monodromy groups of smooth hypersurfaces [3]. The main ingredient in the proof is a Picard–Lefschetz type formula for a suitable degeneration of this family. PubDate: Mon, 20 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw342 Issue No:Vol. 2018, No. 11 (2017)

Authors:Mustaţă M; Popa M. Pages: 3587 - 3605 Abstract: We prove results concerning the behavior of Hodge ideals under restriction to hypersurfaces or fibers of morphisms, and addition. The main tool is the description of restriction functors for mixed Hodge modules by means of the $V$-filtration. PubDate: Mon, 20 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw343 Issue No:Vol. 2018, No. 11 (2017)

Authors:Mongardi G; Pacienza G. Pages: 3606 - 3620 Abstract: In this note, we characterize polarized parallel transport operators on irreducible holomorphic symplectic varieties which are deformations of generalized Kummer varieties. We then apply such characterization to show the existence of ample uniruled divisors on these varieties and derive some interesting consequences on their Chow group of 0-cycles. PubDate: Mon, 20 Feb 2017 00:00:00 GMT DOI: 10.1093/imrn/rnw346 Issue No:Vol. 2018, No. 11 (2017)