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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
6
votes
2
answers
455
views
Powers of elements in an Artinian Ring
Let $R$ be an local Artinian ring, with maximal ideal $\mathfrak{m}$.
Let $e$ be the smallest positive integer for which $\mathfrak{m}^e=(0)$.
Let $t$ be the smallest positive integer for which $x^t …
0
votes
1
answer
493
views
Closed immersion of closed fiber?
Suppose $f: X \rightarrow Y$ is a morphism of schemes, and $y \in Y$ is closed point.
We know the first projection morphism $p_1: X \ $ x$_{Y} \ k(y) \rightarrow X$ is a homeomorphism onto $f^{-1}(y …