# Tagged Questions

**3**

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**0**answers

155 views

### Semistable minimal model of a $K3$-surface and the special fibre

Suppose that $K$ is a $p$-adic field, that is a field of characteristic $0$ whose ring of integers is a complete discrete valuation ring $\mathcal O_K$ and with residue field $k$ (algebraic closed) of ...

**1**

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**0**answers

149 views

### lefschetz hyperplane theorem in positive characteristic

The proof of the Lefschetz Hyperplane theorem over $\mathbb{C}$ is well-known, and relies on Hodge theory in an important way. Does there exist an analogue of this theorem in positive characteristic, ...

**8**

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**0**answers

310 views

### Torelli-like theorem for K3 surfaces on terms of its étale cohomology

Is there a proof of a Torelli-like Theorem for a K3-surface over any field (non complex) in terms of its etale or crystalline cohomology?
For example: If $K\ne \mathbb{C} $ and $X\rightarrow ...

**4**

votes

**1**answer

367 views

### Analogue of Tate or Hodge conjecture for varieties over $\Q_p$

I've been learning about p-adic Hodge theory recently (I'm a beginner), and I've been wondering about the following question the past couple of weeks. Sorry for the long setup, it's mainly ...

**0**

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**1**answer

196 views

### Submodule of a Kisin module

By M. Kisin, let $k$ be an algebraically closed field of characteristic $p$, and $K$ be a totally ramified extension of $B(k)$, the fraction field of the Witt vector ring $W(k)$, the category of ...