Related papers: Frobenius semisimplicity for convolution morphisms

Let $H$ be a connected spherical subgroup of a semisimple algebraic group $G$. In this paper, we give a criterion for $H$-orbit closures in the flag variety of $G$ to have nice geometric and cohomological properties. Our main tool is the…

Let $X$ be a smooth projective algebraic variety over $Z/p$, which has a flat lift to a scheme $X'$ over $Z/p^2$. If the absolute Frobenius morphism $F$ on $X$ lifts to a morphism on $X'$, then an old trick by Mazur shows that push-down of…

We give a criterion for extending a generically semisimple (not necessarily conformal) Frobenius manifold locally near a smooth point of the discriminant to a cohomological field theory. As an application, we show that a large set of…

In this paper, which is the sequel to arXiv:1410.3742, we study the Frobenius pushforward of the structure sheaf on the adjoint varieties in type ${\bf A}_3$ and ${\bf A}_4$. We show that this pushforward sheaf decomposes into a direct sum…

We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules. This is motivated by the Nakayama conjecture and an approach of Martinez-Villa to the Auslander-Reiten conjecture…

We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines the structure of a Levi-flat…

The eigenvalues of Frobenius acting on $\ell$-adic cohomology of a complete intersection over a finite field have the divisibility predicted by the theorem of Ax and Katz. We have corrected some unforgivable typos.

Let \pi : V \rightarrow M be a (real or holomorphic) vector bundle whose base has an almost Frobenius structure (\circ_{M},e_{M}, g_{M}) and typical fiber has the structure of a Frobenius algebra (\circ_{V},e_{V},g_{V}). Using a connection…

Let $X/\mathbb{C}$ be a smooth variety with simple normal crossings compactification $\bar{X}$, and let $L$ be an irreducible $\overline{\mathbb{Q}}_{\ell}$-local system on $X$ with torsion determinant. Suppose $L$ is cohomologically rigid.…

We show that complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups, satisfy a categorical version of the Baum-Connes conjecture with trivial coefficients. This approach, based on…

This article is the first one of a series of three articles devoted to direct images of isocrystals: here we consider isocrystals without Frobenius structure; in the second one (resp. the third one), we will introduce a Frobenius structure…

Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A…

A fundamental theorem of P. Deligne (2002) states that a pre-Tannakian category over an algebraically closed field of characteristic zero admits a fiber functor to the category of supervector spaces (i.e., is the representation category of…

We study the preservation of semisimplicity for holonomic D-modules with respect to the direct and inverse image of mainly finite maps $\pi : X \to Y$ of smooth varieties. A natural filtration of the direct image $\pi_+({\mathcal O}_X)$ is…

Motivated by the analogy between number fields and function fields, this paper extends the main result of \cite{janbazi2025unified} to the function field setting. Let $C$ be a smooth affine curve over a finite field, and let $\pi: S…

This paper studies affine Deligne-Lusztig varieties $X_{\tw}(b)$ in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of $X_{\tw}(b)$ for a minimal length element $\tw$ in the conjugacy…

We show the Frobenius pullback of a general semi-stable vector bundle in the moduli space of vector bundles with fixed rank and degree is still semi-stable by deformation trick. We then present several applications of the main theorem.

This work concerns maps of commutative noetherian local rings containing a field of positive characteristic. Given such a map $\varphi$ of finite flat dimension, the results relate homological properties of the relative Frobenius of…

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a…

We investigate the injectivity of the Frobenius map on thickenings of smooth varieties in projective space over a field of positive characteristic. We obtain uniform bounds -- i.e., independent of the characteristic -- on the thickening…