Epsilon常数与Arakelov欧拉示性数

Epsilon常数与等变Arakelov欧拉示性数

Epsilon constants and equivariant Arakelov Euler characteristics

研究了支持有限群G的驯服作用的算术簇上厄米层的等变Arakelov-欧拉示性数.群作用的驯服使我们能够在一个特别精细的“射影”算术类群中产生一个等变的阿拉克洛夫-欧拉示性数。然后，我们表明，等变的Arakelov-欧拉示性数的各种复杂的微分确定的L-功能的动机从算术品种使用辛表示的群G的的常数。我们的结果可以被视为第一个高维版本的Cassou-Noguès泰勒辛Artin根数的厄米结构的整数环的特征，其次作为一个有符号的等变版本的布洛赫导体公式。

Local epsilon-isomorphisms for rank two p-adic representations of Gal(overline{Q}_p/Q_p) and a functional equation of Kato's Euler system

In this article, we prove (many parts of) the rank two case of the Kato's local epsilon-conjecture using the Colmez's p-adic local Langlands correspondence for GL_2(Q_p). We show that a Colmez's pairing defined in his study of locally algebraic vectors gives us the conjectural epsilon-isomorphisms for (almost) all the families of p-adic representations of Gal(overline{Q}_p/Q_p) of rank two, which satisfy the desired interpolation property for the de Rham and trianguline case. For the de Rham and non trianguline case, we also show this interpolation property for the "critical" range of Hodge-Ta…

叶空间上的数论与动力系统

Number theory and dynamical systems on foliated spaces

我们讨论了具有一维叶理的空间上的数论和动力系统理论之间的类比。重点是比较解析数论的“显式公式”与某些动力学Lefschetz迹公式。本文还指出了Arakelov-欧拉示性数与Connes意义下的欧拉示性数之间的一种可能的关系。最后，解释了广义广义非线性相空间在图像中的作用。

Galois-module theory for wildly ramified covers of curves over finite fields

Given a Galois cover of curves over $\mathbb{F}_p$, we relate the $p$-adic valuation of epsilon constants appearing in functional equations of Artin L-functions to an equivariant Euler characteristic. Our main theorem generalises a result of Chinburg from the tamely to the weakly ramified case. We furthermore apply Chinburg's result to obtain a `weak' relation in the general case. In the Appendix, we study, in this arbitrarily wildly ramified case, the integrality of $p$-adic valuations of epsilon constants.

Special L-values of geometric motives

This paper proposes a conjecture on special values of L-functions of geometric motives over Z. This includes L-functions of mixed motives over Q and Hasse-Weil zeta-functions of schemes over Z. We conjecture the following: the order of L(M, s) at s=0 is given by the negative Euler characteristic of motivic cohomology of $M^\vee(-1)$. Up to a nonzero rational factor, the L-value at s=0 is given by the determinant of the pairing of Arakelov motivic cohomology of M with the motivic homology of M. Under standard assumptions concerning mixed motives over Q, $F_p$, and Z, this conjecture is essentia…