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Results tagged with ag.algebraic-geometry
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user 10147
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
17
votes
Accepted
What is the theory of local rings and local ring homomorphisms?
If you know the objects of a geometric theory then you also know its morphisms because $\mathbb{T}(\mathbf 2,\mathcal E)\simeq [\mathbf 2,\mathbb{T}(\mathcal E)]$. This is Lemma 4.2.3 in Chapter B of …
- 441
11
votes
Accepted
What conditions are needed for $-\otimes_A B$ to be faithful?
The functor you mention is faithful if and only if the functor $-\bigotimes_A B :A-mod\to A-mod$ is faithful, ie iff $B$ is a faithful $A$-module.
For a concrete counterexample take $f:\mathbb{Z}\to …
- 441