Research
Research
Research
Research
1,571+ open-access research outputs.
We construct bounded, commuting projections for the three-dimensional de Rham complex with the additional property that the projections preserve the trace of functions/fields if the latter is a piecew…
In this paper we study the class of \emph{split Nakamura manifolds}, which are a type of solvmanifolds generalizing Nakamura's threefold, defined as quotients of the semidirect product $\mathbb{C}^n \…
We prove the Mukai conjecture on the characterisation of products of projective spaces among Fano varieties for a class of locally factorial Fano varieties defined in terms of their Cox rings. The Fan…
Let $\mathbf{B}_{\mathrm{dR}}^{+, \dagger} \subset \mathbf{B}_{\mathrm{dR}}^{+}$ be the ``convergent" de Rham period ring which is the (un-completed) stalk at the de Rham point of the Fargues--Fontain…
Let $C$ be a smooth projective curve of genus $g \geq 2$ over $\mathbb C$, and let $E^0$ be a vector bundle on $C$. We investigate the birational geometry of the Quot scheme ${\rm Quot}_C(E^0, k, n)$,…
The space of de Rham currents supported in finitely many points in a Lie group $G$ has the structure of a filtered differential graded Hopf algebra. The product is given by convolution of compactly su…
Let $k$ be a field of characteristic $p,$ and $f : X \to S$ a smooth proper morphism of smooth $k$-schemes. Katz's formula gives a relationship between the Kodaira--Spencer map of $f,$ and an invarian…
In this article, we introduce a transverse averaging operator for basic forms on a Riemannian foliation equipped with an isometric transverse Lie algebra action, under the assumption that the leaf clo…
We consider the simplicial de Rham complex and the \v{C}ech-de Rham complex, two bigraded Hilbert complexes whose Hodge-Laplace problems govern spatially coupled problems in mixed dimension and homoge…
Path geometries provide a geometric encoding of systems of second order ODE, which serves as a model for the geometric theory of more general systems of ODE and for cone structures. They are an instan…
We show that hyperplane sections of strongly formal manifolds inherit strong formality. In particular, this property holds for generalized complete intersections defined by positive line bundles with …
In the previous paper of the author, motivated by the categorical $p$-adic local Langlands correspondence, the author studied families of $G_K$-equivariant vector bundles over the Fargues-Fontaine cur…
We construct and compare three D-module models for the minimal representation of the conformal group of an even-dimensional quadratic space. Let $V$ be a quadratic space over a field $\kappa$ of chara…
We investigate infinite-level Shimura varieties within the framework of analytic stacks of Clausen-Scholze, developing their smooth, completed, locally analytic, and de Rham realizations. We formulate…
We construct left, right and bilateral fundamental solutions for generalized steady Stokes' operators $S$ with smooth coefficients coefficients, associated with the de Rham complex of differentials on…
In this article, we consider extended tame persistence commutative differential graded algebras (CDGAs) associated with relative Sullivan algebras. In particular, if the relative Sullivan algebra is a…
We study the Hodge-to-de Rham spectral sequence for integral projective curves with local complete intersection singularities. We prove that degeneration at the E2-page is equivalent to requiring ever…
We prove that the relative p-adic monodromy theorem holds over a dense open subset. Moreover, we establish the equivalence of the following two statements: the local constancy of the Newton polygon fu…
We give an example of proper smooth fourfold over a perfect field k of characteristic p > 0 with asymmetric Hodge--Witt numbers in total degree 3. Our example is sharp both in terms of dimension and t…
In this work, we construct high-order finite element spaces for the $L^2$ de Rham complex on triangular meshes amenable to low-order-refined preconditioning. The spaces are constructed using the Duffy…
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