Related papers: Stability of holonomicity over quasi-projective va…

We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…

We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…

We show that, given a complete Liouville manifold, any homogeneous quasi-morphism on its Hamiltonian group, which satisfies a strengthened version of Hofer continuity called stability, must vanish. This partially addresses a conjecture due…

A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments).

We introduce and study the notion of conic stability of multivariate complex polynomials in $\mathbb{C}[z_1,\ldots, z_n]$, which naturally generalizes the stability of multivariate polynomials. In particular, we generalize Borcea's and…

Let $k$ be a field of characteristic zero containing all roots of unity and $K=k((t))$. We build a ring morphism from the Grothendieck group of semi-algebraic sets over $K$ to the Grothendieck group of motives of rigid analytic varieties…

We establish the foundations of the theory of persistent cohomology operations, derive decomposition formulas for wedge sums and products, and prove their Gromov-Hausdorff stability. We use these results to construct pairs of Riemannian…

We consider germs of holomorphic vector fields with an isolated singularity at the origin $0\in\mathbb{C}^2$. We introduce a notion of stability, similar to "Lyapunov stability". For such a germ, called $L$-stable singularity, either the…

Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…

Using the localization property, we construct a triangulated category of motives over quasi-projective T-schemes for any coefficient where T is a noetherian separated scheme, and we prove the Grothendieck six operations formalism. We also…

This paper is concerned with the complexity and stability of arithmetic operations in the jacobian variety of curves over the field of complex numbers, as the genus grows to infinity. We focus on modular curves. Efficient and stable…

We consider Vinberg $\theta$-groups associated to a cyclic quiver on $k$ nodes. Let $K$ be the product of the general linear groups associated to each node. Then $K$ acts naturally on $\oplus \text{Hom}(V_i, V_{i+1})$ and by Vinberg's…

In this paper we explore a relationship between the topology of the complex hyperplane complements $\mathcal{M}_{BC_n} (\mathbb{C})$ in type B/C and the combinatorics of certain spaces of degree-$n$ polynomials over a finite field…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $k$ its residual field, $\mathcal{P}$ a proper smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $T$ a divisor of $P$, $U:=P\setminus T$, $Y$ a…

For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect…

We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module…

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

This article fills some gaps in Voevodsky's construction of the Steenrod operations acting on the motivic cohomology with coefficients in Z/lZ of motivic spaces in the sense of Morel and Voevodsky over a perfect field of characteristic…

Using constructions of Voisin, we exhibit a smooth projective variety defined over a number field k and two complex embeddings of k, such that the two complex manifolds induced by these embeddings have non isomorphic cohomology algebras…

In our previous study of duality for complete discrete valuation fields with perfect residue field, we treated coefficients in finite flat group schemes. In this paper, we treat abelian varieties. This in particular implies Grothendieck's…