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Fields of characteristic $p$, i.e., fields for which there is a prime $p$ such that $px=0$ for each $x$. Do not use this tag for questions on characteristic polynomials of a matrix.

2 votes
0 answers
96 views

Composing equal characteristic and mixed characteristic deformations

Suppose $k$ is an algebraically closed field of characteristic $p>0$ and $A$ is a $k$-point on a moduli space of certain objects over $k$. Suppose, moreover, that $A$ deforms to a $k[[t]]$-point $B$ a …
Huy Dang's user avatar
  • 245
12 votes
2 answers
879 views

Residues of $\frac{1}{\prod_{i=1}^n (x-P_i)^{e_i}}$

This is a problem occurring in my research about deformations of $\mathbb{Z}/p^n$-covers over a ring of power series. Given an algebraically closed field $k$ of characteristic $p>0$, suppose $1< e_i < …
Huy Dang's user avatar
  • 245
5 votes
0 answers
212 views

Exact differential forms in characteristic $p>0$

Let $k$ be an algebraically closed field of characteristic $p>0$. Suppose $1< e_i <p$ for $i=1,2, \ldots, n$ are integers ($n \ge 2$). What are the conditions on the $e_i$'s so that the rational funct …
Huy Dang's user avatar
  • 245