Related papers: B\'ezoutians and the $\mathbb{A}^1$-degree

Using the classical universal coefficient theorem of Rosenberg-Schochet, we prove a simple classification of all localizing subcategories of the Bootstrap category of separable complex C*-algebras. Namely, they are in bijective…

In a recent preprint, Gullerud and Walker [2] proved a theorem and made a conjecture about the correctness of efficiently generating B\'ezout trees for Pythagorean pairs. In this note, we give a simple proof of their theorem, confirm that…

For a cuspidal automorphic representation of GL2/Q associated to a modular form, the local and global Langlands correspondences are compatible at all finite places of Q. On the p-adic Coleman-Mazur eigencurve this principle can fail (away…

We extend the stable motivic homotopy category of Voevodsky to the class of scalloped algebraic stacks, and show that it admits the formalism of Grothendieck's six operations. Objects in this category represent generalized cohomology…

A basic problem in the study of algebraic morphisms is to determine which sets can be realised as the image of an endomorphism of affine space. This paper extends the results previously obtained by the first author on the question of…

For two differentiable maps between two manifolds of possibly different dimensions, the local and global coincidence homology classes are introduced and studied by Bisi- Bracci-Izawa-Suwa (2016) in the framework of Cech-de Rham cohomology.…

We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish…

We use a counting argument and surgery theory to show that if $D$ is a sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a $d$-sheeted cover…

We show that a certain subspace of space of elliptic cusp forms is isomorphic as a Hecke module to a certain subspace of space of Jacobi cusp forms of degree one with matrix index by constructing an explicit lifting. This is a partial…

In a recent paper, Colliot-Th\'el\`ene, Parimala and Suresh conjectured that a local-global principle holds for projective homogeneous spaces of connected linear algebraic groups over function fields of p-adic curves. In this paper, we show…

Brumer and Kramer gave bounds on local conductor exponents for an abelian variety $A/\mathbb Q$ in terms of the dimension of $A$ and the localization prime $p$. Here we give improved bounds in the case that $A$ has maximal real…

In this paper, we treat $\mathscr{D}$-modules on the basic affine space $G/U$ and their global sections for a semisimple complex algebraic group $G$. Our aim is to prepare basic results about large non-irreducible modules for the branching…

We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree.…

We consider regular endomorphisms of the complex affine space with a degree gap $k$. They are endomorphisms $f$ of $\mathbb{A}_{\mathbb{C}}^{N}$ of the form…

We construct the universal monodromic big tilting sheaf on base affine space and calculate its endomorphisms. By formal completion, we recover Soergel's pro-unipotent Endomorphismensatz with arbitrary field coefficients. We give a Soergel…

We find a relationship between the global dimension of an algebra $A$ and the global dimension of the endomorphism algebra of a $\tau$-tilting module, when $A$ is of finite global dimension. We show that, in general, the global dimension of…

We consider equivariant versions of the motivic Chern and Hirzebruch characteristic classes of a quasi-projective toric variety, and extend many known results from non-equivariant to the equivariant setting. The corresponding generalized…

Following Eilenberg-Steenrod axiomatic approach we construct the universal ordinary homology theory for any homological structure on a given category by representing ordinary theories with values in abelian categories. For a convenient…

We provide a characterization of infinite algebraic Galois extensions of the rationals with uniformly bounded local degrees, giving a detailed proof of all the results announced in a paper by Checcoli and Zannier and obtaining relevant…

We define a category of planar diagrams whose Grothendieck group contains an integral version of the infinite rank Heisenberg algebra, thus yielding a categorification of this algebra. Our category, which is a q-deformation of one defined…