Invariants Associated to Orthogonal $ε$-constants

$ε$-Constants and Orthogonal Representations

In this paper we suppose G is a finite group acting tamely on a regular projective curve X over Z and V is an orthogonal representation of G of dimension 0 and trivial determinant. Our main result determines the sign of the $ε$-constant $ε(X/G,V)$ in terms of data associated to the archimedean place and to the crossing points of irreducible components of finite fibers of X, subject to certain standard hypotheses about these fibers.

Weil表示的不变量与符号为(2,2)的正交群的模单位

Invariants for the Weil representation and Modular Units for Orthogonal Groups of Signature (2,2)

该研究证明了含自迷向子群的判别群的Weil表示不变量空间由自迷向子群特征函数张成，并应用该结果通过Borcherds乘积构造了符号(2,2)正交群的模单位。

范数正交基与$p$-adic格的不变量

Norm Orthogonal Bases and Invariants of $p$-adic Lattices

本文证明每个p-adic格存在正交基，定义连续极大值与逃逸距离，给出多项式时间算法求解LVP和CVP，并证明正交化与CVP多项式等价。

Invariants and discriminant ideals of orthogonal complements in a quadratic space

This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of such a complement in the sense of Shimura. The other is to investigate an ideal of the base field, which may be viewed as a difference between the genus of maximal lattices and an integral lattice in the complement. We shall discuss about the class number of the genus of maximal lattices as an application.

The Arason invariant of orthogonal involutions of degree 12 and 8, and quaternionic subgroups of the Brauer group

Using the Rost invariant for torsors under Spin groups one may define an analogue of the Arason invariant for certain hermitian forms and orthogonal involutions. We calculate this invariant explicitly in various cases, and use it to associate to every orthogonal involution with trivial discriminant and trivial Clifford invariant over a central simple algebra of even co-index a cohomology class $f_3$ of degree 3 with $μ_2$ coefficients. This invariant $f_3$ is the double of any representative of the Arason invariant; it vanishes when the algebra has degree at most 10, and also when there is a q…

I^3=0的域上的正交对合

Orthogonal involutions over fields with I^3=0

本研究针对特征不为2且I^3F=0的基域F，推导了带典范对合的四元数代数上斜埃尔米特型的u不变量的上界，上界由基域的u不变量表出。