Geometric description of the connecting homomorphism for Witt groups

Hermitian K-理论的连接同态

The connecting homomorphism for Hermitian $K$-theory

本文利用 Grothendieck 留数复形发展 Hermitian K-理论的前推与拉回，几何解释其连接同态，并据此计算正则射影丛和 Grassmann 簇的 Hermitian K-理论、给出显式基。

二维Kummer--Artin--Schreier--Witt型核的Cartier对偶

Cartier Duals of Two-Dimensional Kummer--Artin--Schreier--Witt Type Kernels

本文研究二维Kummer--Artin--Schreier--Witt型同态核的Cartier对偶，在幂零条件下给出其用Witt向量表示的显式描述，并利用Sekiguchi--Suwa方法和形式完备化分析完成证明。

Witt groups of spinor varieties

We show that Witt groups of spinor varieties (aka.\ maximal isotropic Grassmannians) can be presented by combinatorial objects called even shifted young diagram. Our method relies on the Blow-up setup of Balmer-Calmès, and we investigate the connecting homomorphism of the localization sequence via the projective bundle formula of Walter-Nenashev, the projection formula of Calmès-Hornbostel and the excess intersection formula of Fasel.

Zeta functions, Grothendieck groups, and the Witt ring

We prove some results connecting the zeta functions of varieties over finite fields with the big Witt ring over $\mathbb Z$. We explore relations with motivic measures and a classical formula of Macdonald on invariants of symmetric products of a variety.

光滑实曲线与曲面的Witt群

Witt groups of smooth real curves and surfaces

本文研究光滑实代数曲线与曲面的Witt群，拓展Monnier、Sujatha相关工作，计算$\boldsymbol{C}/\boldsymbol{R}$转移，应用方法得到$\boldsymbol{R}$上维数≤3的光滑非等轴二次型的移位与扭曲Witt群。

From the global signature to higher signatures

Let $X$ be an algebraic variety over the field of real numbers $\mathbb{R}$. We use the signature of a quadratic form to produce "higher" global signatures relating the derived Witt groups of $X$ to the singular cohomology of the real points $X(\mathbb{R})$ with integer coefficients. We also study the global signature ring homomorphism and use the powers of the fundamental ideal in the Witt ring to prove an integral version of a theorem of Raman Parimala and Jean Colliot-Thelene on the mod 2 signature. Furthermore, we obtain an Atiyah-Hirzebruch spectral sequence for the derived Witt groups of…