# Tagged Questions

**3**

votes

**1**answer

346 views

### weight monodromy conjecture for curves?

Hi,
Is there a simple proof of the weight monodromy conjecture in the case of a curve over a mixed characteristic local field?
Thanks!

**15**

votes

**1**answer

717 views

### On the Hasse-Weil L-function of $P^n$

So let us start with the "simplest" scheme over $Spec(\mathbf{Z})$ namely $X_0=Spec(\mathbf{Z})$. Then the (reciprocal) Weil zeta function of $X_0$ at a prime $p$ is given by $Z_p(T)=1-T$ (a ...

**5**

votes

**2**answers

854 views

### Direct proof of special case of Hasse's theorem for elliptic curves

Consider the elliptic curve $y^2 = x^3 + x$ over $\mathbb{F}_p$, where $p \equiv 1 \pmod 4$.
If memory serves correctly, the number of points (excluding the point at infinity) is $p - a$ where $a$ is ...