Dingxin Zhang

activity

20232026

collaborators

8 papers

math.NT2026

Exotic and inverted Kloosterman sums over semisimple algebras

Daqing Wan, Dingxin Zhang

We introduce exotic Kloosterman sums and exotic inverted Kloosterman sums attached to non-commutative finite-dimensional semisimple algebras over a finite field $F_{q}$ , and…

math.AG2026

Classical and irregular Hodge numbers

Yichen Qin, Dingxin Zhang

Let $U$ be a smooth quasi-projective complex variety with a regular function $f$ . The twisted de Rham cohomology groups $H_{dR}^{k} (U, f)$ carry the decreasing irre…

math.AG2026

Asymptotic Betti bounds for hypersurfaces in a singular variety

Xuanyu Pan, Dingxin Zhang, Xiping Zhang

We show that for any degree $d$ hypersurface $Y \subset X$ in a possibly singular projective variety $X \subset P^{N}$ , the total Betti number of $Y$ is bounded by $3\text{d…

math.AG2026

Weil conjectures and affine hypersurfaces

Dingxin Zhang

We give yet another proof of the Riemann hypothesis for smooth proper varieties over a finite field (Deligne's theorem), by reducing to the hypersurface case. The latter was establ…

math.AG2025

Betti number bounds for varieties and exponential sums

Daqing Wan, Dingxin Zhang

Using basic properties of perverse sheaves, we give new upper bounds for compactly supported Betti numbers for arbitrary affine varieties in $A^{n}$ defined by $r$ polynomia…

math.AG2024

On sums of Betti numbers of affine varieties

Dingxin Zhang

We show that if V is a subvariety of the affine N-space defined by polynomials of degree at most d, then the sum of its $ℓ$ -adic Betti numbers does not exceed $2(N + 1)^{2N +1}(…

math.AG2024

Generic Triviality of Automorphism Groups of Complete Intersections

Renjie Lyu, Dingxin Zhang

We prove in most cases that a general smooth complete intersection in the projective space has no non-trivial automorphisms.

math.AG2023

Hodge and Frobenius colevels of algebraic varieties

Daqing Wan, Dingxin Zhang

We provide new, improved lower bounds for the Hodge and Frobenius colevels of algebraic varieties (over $C$ or over a finite field) in all cohomological degrees. These bou…