# Tagged Questions

**0**

votes

**0**answers

160 views

### Hodge structure of abelian surfaces

In my case, I have an abelian surface $A$ of (2,8)-polarization, and I have some finite group (may not be abelian group) $G$ acting on $A$ without fixed point. I want to understand when there is a ...

**5**

votes

**1**answer

365 views

### Mumford-Tate groups of abelian varieties with potentially good reduction everywhere

Let $A$ be an abelian variety defined over a number field, and let $MT(A)$ be its Mumford-Tate group. It is a conjecture of Morita that if $MT(A)$ is anisotropic-mod-center (that is, it has no ...

**6**

votes

**1**answer

516 views

### Mumford-Tate group and Galois representations

Could someone please point me towards a proof of why the image of a Galois representation on the Tate-module of an abelian variety is limited by its Mumford-Tate group?

**1**

vote

**1**answer

480 views

### Abelian varieties of CM type?

Is there any introduction to abelian varieties of CM type?any reference?Like how to construct a abelian varieties given a CM field E?What is the properites of the Mumford Tate group of the abelian ...

**17**

votes

**4**answers

2k views

### Why do people think that abelian varieties are the hardest case for the Hodge conjecture?

Today, I heard that people think that if you can prove the Hodge conjecture for abelian varieties, then it should be true in general. Apparently this case is important enough (and hard enough) that ...