Computations of Chow-Witt groups for split quadrics and other smooth varieties

Chow-Witt群是经典Chow群的加细。 它们包含了代数簇的重要不变量。 例如，它们包含“欧拉类”，它编码仿射基上向量丛的分裂行为。这个项目的目的是计算某些光滑簇族的Chow-Witt群。我们最初的重点将是分裂二次曲面，这些承诺的结果有影响的经典问题的平方和公式的存在。接下来，我们将研究其他类型的例子（其他齐性空间，光滑曲线，.）。在这些空间中，维特群和埃尔米特K-群已经被部分理解，而Chow-Witt群通过motivic谱序列与它们密切相关。

Chow-Witt groups are refinements of the classical Chow groups. They contain important invariants of algebraic varieties. For example, they contain the "Euler class", which encodes the splitting behaviour of vector bundles over affine bases. The aim of this project is to compute the Chow-Witt groups of certain families of smooth varieties. Our initial focus will be on split quadrics, as results for these promise to have implications for the classical problem of the existence of sums-of-squares formulas. Next, we will investigate other classes of examples (other homogeneous spaces, smooth curves, ...). The Witt groups and the hermitian K-groups are already partially understood for these spaces, and the Chow-Witt groups are closely related to these via motivic spectral sequences.