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Results tagged with ac.commutative-algebra
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user 100511
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
5
votes
2
answers
500
views
Finite maps and jacobian condition
Let $k$ be an algebraically closed field and take $f_{1}, ..., f_{n} \in k[X_{1},..., X_{n}]$ with the jacobian condition: $\det J_{f} = 1$. Let $A:= k[X_{1},...,X_{n}]/(f_{1},...,f_{n})$ and conside …
- 348
8
votes
0
answers
572
views
Polynomial maps over $\mathbb{Z}$
It is know that an injective polynomial map $f:\overline{\mathbb{Q}}^{n} \longrightarrow \overline{\mathbb{Q}}^{n}$ is an bijection with inverse regular (Cynk-Rusek theorem). My question is following: …
- 348
-1
votes
1
answer
177
views
About n-tuple unimodular
Let ($\mathcal{O}$, $\mathcal{M}$, k) be an DVR and $F_{1},...,F_{n} \in \mathcal{O}[X_{1},...,X_{n}]$ such that detJF = 1 where JF is the matrix $(\frac{\partial F_{i}}{\partial X_{j}})$. Suppose the …
- 348
6
votes
Accepted
Connection between the Jacobian Conjecture and number theory conjectures
An interesting conjecture that has relation with the Jacobian Conjecture is the following:
Let $(\mathcal{O},\mathcal{M},k)$ be a complete discrete valuation ring with k finite.Let $f_{1},...,f_{n …
- 348