# Tagged Questions

301 views

### Local factors of Hasse-Weil zeta function - what do they have in common?

Let $X$ be a regular scheme, flat and of finite type over $Spec(\mathbb{Z})$ (add "projective" if you want). Then the Hasse-Weil zeta function of $X$ is defined as a product over all prime numbers of ...
224 views

### Elliptic units and Euler system

Maybe this question is quite obscure and ambiguous. I am really sorry for such ambiguity. My question is, what is the good thing we get from defining elliptic units and Euler system? There are lots ...
690 views

### Generalizing Eichler-Shimura to higher dimension, again

This question is related to Intuition behind the Eichler-Shimura relation? and L-functions and higher-dimensional Eichler-Shimura relation Answering the first question above, Matt Emerton gives a ...
552 views

### impact of Poincaré duality on functional equation

Given a variety $X/\mathbf{F}_q$ and a sheaf $\mathcal{F}$ on it, what is the relation of $L(X,\mathcal{F},T)$ and $L(X,D(\mathcal{F}),T)$?
882 views

### Arithmetic geometry from a bird's-eye view

Is ist true that Arithmetic Geometry can roughly be separated into two areas: 1) Showing that motivic $L$-functions are automorphic. 2) Calculating special values of these $L$-functions.
644 views

### Rankin-Selberg convolutions of motivic L-series

Background: Let $M_{f_i}, i=1,2$ be two modular motives associated to cusp forms $f_i \in S_{w_i}(\Gamma_0(N_i))$ of weight $w_i$ and level $N_i$ respectively. The Rankin-Selberg convolution ...
1k views

### What are “fractional motives”?

Kirti Joshi's musings mention "fractional motives". Do you know what are they good for and what the current state of constructions is for them? Edit: Further cases of "fractional motives" as ...
Suppose $E/\mathbb{Q}$ is an elliptic curve with rank zero. According to the conjecture of Birch and Swinnerton-Dyer, the special value $L(1,E_{/\mathbb{Q}})$ should be equal (up to some harmless ...