Related papers: Projectivity of the Witt vector affine Grassmannia…

Given a sheaf of unital commutative and associative algebras A, first we construct the k-th Grassmann sheaf G_A(k,n) of A^n whose sections induce vector subsheaves of A^n of rank k. Next we show that every vector sheaf over a paracompact…

Let X be a smooth complex irreducible projective variety of dimension $n \geq 2$ and $H$ be an ample line bundle on $X$. In this paper, we construct families of $\mu_H$-stable vector bundles on $X$ having fixed determinant and rank $r$,…

In this paper, we explore an abstraction of uniform integrability in vector lattices and demonstrate its application by providing a positive solution to an open question posed by Kuo, Rodda, and Watson. Specifically, we show that for finite…

Let k be a field of positive characteristic. We construct, for each dominant coweight \lambda of the standard maximal torus in the special linear group, a closed subvariety D(\lambda) of the multigraded Hilbert scheme of an affine space…

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…

The Grassmannian is an important object in Algebraic Geometry. One of the many techniques used to study the Grassmannian is to build a vector space from its points in the projective embedding and study the properties of the resulting linear…

The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show…

In this paper, we examine the behavior of ideal-adic separatedness and completeness under certain ring extensions using trace map. Then we prove that adic completeness of a base ring is hereditary to its ring extension under reasonable…

The affine Grassmannian of $SL_n$ admits an embedding into the Sato Grassmannian, which further admits a Pl\"ucker embedding into the projectivization of Fermion Fock space. Kreiman, Lakshmibai, Magyar, and Weyman describe the linear part…

This paper contains three parts. In the first part, we give a thorough overview of the theory of Artin-Schreier-Witt extensions: this theory allows one to understand the $\mathbf{Z}/p^n\mathbf{Z}$-extensions of any field $K$ of…

A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…

Let $X$ be a non-singular quasi-projective variety over a field, and let $\mathcal E$ be a vector bundle over $X$. Let $\mathbb G_X({d}, \mathcal E)$ be the Grassmann bundle of $\mathcal E$ over $X$ parametrizing corank $d$ subbundles of…

We study the algebraic $K$-theory of smooth schemes over $W_n(\Bbbk)$, where $\Bbbk$ is a perfect field of characteristic $p>0$. For a $p$-adic smooth scheme $X_{\centerdot}$ over $W_{\centerdot}(k)$, we introduce complexes…

Let $\mathcal H$ be a complex Hilbert space and $\mathcal F_s (\mathcal H)$ the real vector space of all self-adjoint finite rank bounded operators on $\mathcal H$. We generalize the famous Wigner's theorem by characterizing linear maps on…

In their paper Scholze and Weinstein show that a certain diagram of perfectoid spaces is Cartesian. In this paper, we generalize their result. This generalization will be used in a forthcoming paper of ours to compute certain non-trivial…

In a previous work the authors gave a conceptual explanation for the linearity of the Weil representation over a finite field k of odd characteristic: There exists a canonical system of intertwining operators between the Lagrangian models…

We demonstrate that Feynman integrals of a fixed diagram form a flat vector bundle over the complement of Landau varieties that possesses a connection \begin{equation} \frac{\partial}{\partial p_{i,\mu}}f_\beta(p_{i,\mu})=\sum_{\beta'}…

Reineke and independent other authors proved that every projective variety arises as a quiver Grassmannian. We prove the claim in the title by restricting Reineke's isomorphism to Grassmannians for a fully exact subcategory.

In 1998 Kleinbock conjectured that any set of weighted badly approximable $d\times n$ real matrices is a winning subset in the sense of Schmidt's game. In this paper we prove this conjecture in full for vectors in $\mathbf{R}^d$ in…

We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by…