Questions tagged [arithmetic-scheme]
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5 questions
3 votes
0 answers
157 views
Logarithmic differentials on an arithmetic surface, and Poincaré residue
Suppose that $X$ is an arithmetic surface, i.e. $\pi: X \to S$ flat and relative dimension 1 over a Dedekind scheme $S$, and assume $X$ smooth. Let $Y \subset X$ be a horizontal effective Cartier ...
- 1,358
2 votes
1 answer
551 views
Linear systems over non-algebraically closed field
Let $X$ be a regular, irreducible projective scheme, of finite type over an arbitrary field $k$. Both Weil divisors and Cartier divisors are defined on $X$ and naturally correspond. If $k$ is ...
- 3,565
7 votes
1 answer
784 views
Is there a category-theoretic definition of the arithmetic Grothendieck group
Let $X$ be a regular scheme which is flat over $\mathbf{Z}$. The arithmetic Grothendieck group $\hat{K}(X)$ is defined to be the quotient of $\hat{G}(X)$ by $\hat{G}^\prime(X)$. This is actually quite ...
- 9,697
15 votes
5 answers
6k views
Examples and intuition for arithmetic schemes
How should a beginner learn about arithmetic schemes (interpret this as you wish, or as a regular scheme, proper and flat over Spec(Z))? What are the most important examples of such schemes? Good ...
6 votes
1 answer
882 views
Existence of proper regular models for varieties over Q and other global fields
What is known about regular proper models for smooth projective varieties over Q? Results for other global fields would also be interesting, as well as general comments and suggested references for ...
- 5,677