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2 votes
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Galois cohomology of cyclotomic extension

Let $K$ be a complete discrete valuation ring with algebraically closed residue field $F$ of characteristic $p > 0$. Suppose ${\Bbb Q}_p \subset K$ and the absolute ramification index v$_{\pi_K}(p) ...
Pierre MATSUMI's user avatar
1 vote
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125 views

galois deformation ring with type is union of irreducible components

Notation: $K$ finite extension of $\mathbb{Q}_p$, $G_K$ absolute Galois group of $K$, $E$ is finite extension of $\mathbb{Q}_p$ (coefficient field), $O_E$ is ring of integer in $E$. In this paper of ...
quasi-mathematician's user avatar
1 vote
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138 views

Power series ring $R[[X_1,\ldots,X_d]]$ over a domain $R$

Let $R$ be a domain and \begin{align*} T \,\colon= R[[X_1,\ldots,X_d]]. \end{align*} Suppose that we have $d$ elements $f_1,\ldots,f_d \in T$ and let us consider an ideal $J$ of $T$ such that $(f_1,\...
Pierre's user avatar
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1 vote
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On the exponent of a certain matrix $A$ in characteristic $p > 0$

Let $A$ be a square matrix in characteristic $p > 0$ with both column and row having length $(1 + p^0 + p + \cdots + p^i)$, where $i \geq 0$. Suppose that further the $(m,n)$-component $a_{m,n}$ ...
Pierre's user avatar
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How geometry changes up to Hermitian inner product on Line bundle (Kodaira embedding)

Riemann metric $g \colon= \Sigma g_{ij} dx_i \otimes dx_j$ on a Kähler manifold $M$ will define the length of a line on $M$, i.e. intrinsic geometry. The line bundle $L$ on $M$ is equipped with a ...
Pierre's user avatar
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116 views

Gauss lemma for a complete Noetherian domain

Suppose that $R$ is a Noetherian complete domain over a field $K$. Suppose that a monic polynomial $f(X) \in R[X]$ (i.e., the highest degree $X^e$ in $f$ has the coefficient $1$), satisfies the ...
Pierre's user avatar
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