Related papers: Wild Ramification and Restrictions to Curves

Ramification for commutative ring spectra can be detected by relative topological Hochschild homology and by topological Andr\'e-Quillen homology. In the classical algebraic context it is important to distinguish between tame and wild…

Using the Riemann Hypothesis over finite fields and bounds for the size of spherical codes, we give explicit upper bounds, of polynomial size with respect to the size of the field, for the number of geometric isomorphism classes of…

The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified case, are differential operators with irregular singularities,…

This is the second part of the paper which proves the compatibility of pushforward along a proper morphism of an \'{e}tale constructible sheaf and the pushforward of its characteristic cycle up to $p$-torsion. In this second part, we show a…

Let $X$ be a smooth algebraic variety over $k$. We prove that any flat quasicoherent sheaf on $\operatorname{Ran}(X)$ canonically acquires a D-module structure. In addition, we prove that, if the geometric fiber $X_{\overline{k}}$ is…

We classify (semi)stable sheaves on a rational curve with one node. The results are based on the classification of indecomposable torsion-free sheaves due to Drozd and Greuel "Tame and wild projective curves and classification of vector…

We investigate the positivity and extension of invertible sheaves on group homogeneous spaces over coherent bases. Bypassing the failure of standard limit arguments and the classical Weil--Cartier correspondence, we develop a valuative…

We construct a vector bundle $E$ on a smooth complex projective surface $X$ with the property that the restriction of $E$ to any smooth closed curve in $X$ admits an algebraic connection while $E$ does not admit any algebraic connection.

Let $\cMx$ be the moduli space of stable vector bundles of rank $n\geq 3$ and determinant $\xi$ over a connected Riemann surface $X$, with $n$ and $d(\xi)$ coprime. Let $D$ be a Calabi-Yau hypersurface of $\cMx$. Denote by $U_D$ the…

We give a simple characterization of the totally wild ramified valuations in a Galois extension of fields of characteristic p. This criterion involves the valuations of Artin-Schreier cosets of the F_{p^r}^\times-translation of a single…

We give an algorithm to determine whether a kernel sheaf over a smooth projective curve over an algebraically closed field is semistable. The algorithm uses symmetric powers to make destabilizing subbundles visible as global sections.

We show that every bad orbifold vector bundle can be realized as the restriction of a good orbifold vector bundle to a suborbifold of the base space. We give an explicit construction of this result in which the Chen-Ruan orbifold cohomology…

We introduce the characteristic class of an l-adic etale sheaf using a cohomological pairing due to Verdier (SGA5). As a consequence of the Lefschetz-Verdier trace formula, its trace computes the Euler-Poincare characteristic of the sheaf.…

We consider the general problem of enumerating branched covers of the projective line from a fixed general curve subject to ramification conditions at possibly moving points. Our main computations are in genus 1; the theory of limit linear…

The ramification of a polyhedral space is defined as the metric completion of the universal cover of its regular locus. We consider mainly polyhedral spaces of two origins: quotients of Euclidean space by a discrete group of isometries and…

In order to study $p$-adic \'etale cohomology of an open subvariety $U$ of a smooth proper variety $X$ over a perfect field of characteristic $p>0$, we introduce new $p$-primary torsion sheaves. It is a modification of the logarithmic de…

For a domestic finite group scheme, we give a direct description of the Euclidean components in its Auslander-Reiten quiver via the McKay-quiver of a finite linearly reductive subgroup scheme of $SL(2)$. Moreover, for a normal subgroup…

This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves E of arbitrary high rank on a general standard (resp. linear) determinantal scheme X\subset \PP^n of codimension…

We consider the category $\operatorname{Qcoh}\mathbb{X}$ of quasicoherent sheaves where $\mathbb{X}$ is a weighted noncommutative regular projective curve over a field $k$. This category is a hereditary, locally noetherian Grothendieck…

We analyse the diagonal quotient for products of certain Artin--Schreier curves. The smooth models are almost always surfaces of general type, with Chern slopes tending asymptotically to 1. The calculation of numerical invariants relies on…