Related papers: Derived Grassmannians and derived Schur functors
We realise Buchweitz and Flenner's semiregularity map (and hence a fortiori Bloch's semiregularity map) as the tangent of a morphism of derived moduli functors. An immediate consequence is that it annihilates all obstructions (not just…
We construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigate the combinatorics of affine Schubert calculus for type $A$. We introduce Murnaghan-Nakayama elements and Dunkl elements in the…
We construct a category of quantum polynomial functors which deforms Friedlander and Suslin's category of strict polynomial functors. The main aim of this paper is to develop from first principles the basic structural properties of this…
We construct a non-$\mathbb{A}^1$-invariant motivic ring spectrum $\mathrm{KO}$ over $\mathrm{Spec}(\mathbb{Z})$, whose associated cohomology theory on qcqs derived schemes is the Grothendieck-Witt theory of classical symmetric forms (as…
We study the relationship between derived categories of factorizations on gauged Landau-Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions on the variation, we show the derived…
Given a vector bundle $\mathcal E$ on a smooth projective variety $B$, the flag bundle $\mathcal F l(1,2,\mathcal E)$ admits two projective bundle structures over the Grassmann bundles $\mathcal G r(1, \mathcal E)$ and $G r(2, \mathcal E)$.…
We give a new construction of the spherical Witt vector functor of Lurie and Burklund-Schlank-Yuan and extend it to nonconnective objects using synthetic spectra and recent work of Holeman. The spherical Witt vectors are used to build…
We continue, generalize and expand our study of linear degenerations of flag varieties from [G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier, M. Reineke, Math. Z. 287 (2017), no. 1-2, 615-654]. We realize partial flag varieties as quiver…
We provide a prorepresenting object for the noncommutative derived deformation problem of deforming a module $X$ over a differential graded algebra. Roughly, we show that the corresponding deformation functor is homotopy prorepresented by…
We give explicit combinatorial descriptions of three Schur functors arising in the theory of pre-Lie algebras. The first of them leads to a functorial description of the underlying vector space of the universal enveloping pre-Lie algebra of…
We study a notion of derived foliations on schemes and derived schemes of arbitrary characteristics. We introduce the Hodge filtration associated to a derived foliation, which functorialy filters derived de Rham cohomology. We use this…
Developing on the ideas of R. Stora and coworkers, a formulation of two dimensional field theory endowed with extended conformal symmetry is given, which is based on deformation theory of holomorphic and Hermitian spaces. The geometric…
We show that canonical bases in $\dot{U}(\mathfrak{sl}_n)$ and the Schur algebra are compatible; in fact we extend this result to $p$-canonical bases. This follows immediately from a fullness result from a functor categorifying this map. In…
In this paper we study the T-equivariant generalized cohomology of flag varieties using two models, the Borel model and the moment graph model. We study the differences between the Schubert classes and the Bott-Samelson classes. After setup…
We develop a theory of tdos and twisted $\mathcal D$-modules over general base schemes with a focus on functorial aspects. In particular, we introduce a flat base change functor and establish its compatibility with globalization and direct…
The aim of this paper is to offer an algebraic construction of infinite-dimensional Grassmannians and determinant bundles (and therefore valid for arbitrary base fields). As an application we construct the $\tau$-function and formal…
We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic…
In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bundles, including isotropic ones. All these formulas are proved in a rather uniform way…
Naisse and Vaz defined an extension of KLR algebras to categorify Verma modules. We realise these algebras geometrically as convolution algebras in Borel-Moore homology. For this we introduce Grassmannian-Steinberg quiver flag varieties.…
In this thesis we study two main topics which culminate in a proof that four distinct definitions of the equivariant derived category of a smooth algebraic group $G$ acting on a variety $X$ are in fact equivalent. In the first part of this…