Related papers: Logarithmic Cartier Transform

According to the Langlands functoriality conjecture, broadened to the setting of spherical varieties (of which reductive groups are special cases), a map between L-groups of spherical varieties should give rise to a functorial transfer of…

In a previous paper, we stated a general almost purity theorem in the style of Faltings: if R is a ring for which the Frobenius maps on finite p-typical Witt vectors over R are surjective, then the integral closure of R in a finite \'etale…

We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew-Hermitian differentiation matrix. While a theory of such L2-orthogonal systems is…

We give two algebro-geometric inspired approaches to fast algorithms for Fourier transforms in algebraic signal processing theory based on polynomial algebras in several variables. One is based on module induction and one is based on a…

Let $\mathscr{O}_K$ be a henselian DVR with field of fractions $K$ and residue field of characteristic $p>0$. Let $S$ denote $\mathop{\mathrm{Spec}} \mathscr{O}_K$ endowed with the canonical log structure. We show that the generic fiber…

This thesis contains results relevant for two different classes of conformal field theory. We partly treat rational conformal field theory, but also derive results that aim at a better understanding of logarithmic conformal field theory.…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ is a (strict) functor taking values in the category of commutative…

We obtain a global version of the Hamiltonian KAM theorem for invariant Lagrangean tori by glueing together local KAM conjugacies with help of a partition of unity. In this way we find a global Whitney smooth conjugacy between a…

Let $K$ be a field of characteristic zero complete for a discrete valuation, with perfect residue field of characteristic $p>0$, and let $K^+$ be the valuation ring of $K$. We relate the log-crystalline cohomology of the special fibre of…

For a regular map $F$ from a complex smooth affine variety $X$ to $\mathbb A^r_\mathbb C$, we construct generalized nearby-cycle modules of a regular holonomic $\mathscr D$-module $\mathcal M$ along log strata with the log structure induced…

Orbifold generalizations of the ordinary and modified melting crystal models are introduced. They are labelled by a pair $a,b$ of positive integers, and geometrically related to $\mathbf{Z}_a\times\mathbf{Z}_b$ orbifolds of local…

We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting.…

Inspired by the log Gromov-Witten (or GW) theory of Gross-Siebert/Abramovich-Chen, we introduce a geometric notion of log J-holomorphic curve relative to a simple normal crossings symplectic divisor defined in [FMZ1]. Every such moduli…

We generalize a result of Orlov and Van den Bergh on the representability of a cohomological functor from the bounded derived category of a smooth projective variety over a field to the category of L-modules, to the case where L is a field…

Let X be a smooth complex projective variety of dimension n equipped with a very ample Hermitian line bundle L. In the first part of the paper, we show that if there exists a toric degeneration of X satisfying some natural hypotheses (which…

Let $X$ be a smooth projective algebraic variety over $Z/p$, which has a flat lift to a scheme $X'$ over $Z/p^2$. If the absolute Frobenius morphism $F$ on $X$ lifts to a morphism on $X'$, then an old trick by Mazur shows that push-down of…

For $X$ a smooth quasi-projective variety and $X^{[n]}$ its associated Hilbert scheme of $n$ points, we study two canonical Fourier--Mukai transforms $D(X)\to D(X^{[n]})$, the one along the structure sheaf and the one along the ideal sheaf…

Using log convergent topoi, %In the derived category of filtered complexes of %sheaves of modules over %an isostructure we define two fundamental filtered complexes $(E_{conv},P)$ and $(C_{conv},P)$ for the log scheme obtained by a smooth…

For any finite group G we define the moduli space of pointed admissible G-covers and the concept of a G-equivariant cohomological field theory (G-CohFT), which, when G is the trivial group, reduce to the moduli space of stable curves and a…