Desvl's blog

Introduction Throughout, let $P(x,y)=x+\frac{1}{x}+y+\frac{1}{y}+1$.

Boolean ring Let $B$ be a commutative ring with unity.

Recall Throughout, let $K$ be a field of characteristic $p\ne 0$ and $E/K$ a cyclic extension of order $p^{m-1}$ with $m >1$.

Introduction Regular local rings are important objects in modern algebra, number theory and algebraic geometry.

Introduction Let $\mathbb{F}_3$ be the field of three elements and $SL_2(\mathbb{F}_3)$ be the group of $2 \times 2$ matrices with determinant $1$.

Introduction Polynomial is of great interest in various fields, such as analysis, geometry and algebra.

Introduction Let $f:\mathbb{C} \to \mathbb{C}$ be a holomorphic function.

Introduction There are a lot of important linear algebraic groups that are widely used in mathematics, physics and industry.

Introduction When studying a linear space, when some subspaces are known, we are interested in the contribution of these subspaces, by studying their sum or (inner) direct sum if possible.

Introduction The classic version of Chinese remainder theorem tells us that we can find solutions out of modulus relations.

Introduction In another post we gave an exposition of irreducible representations of $SO(3)$, where we find ourselves studying harmonic polynomials on a sphere.

Introduction Historically, thanks to Gauss, the quadratic reciprocity law marked the beginning of algebraic number theory.

Introduction In analysis and probability theory, one studies various sort of convergences (of random variables) for various reasons.

Introduction Let $G$ be a locally compact abelian group (for example, $\mathbb{R}$, $\mathbb{Z}$, $\mathbb{T}$, $\mathbb{Q}_p$).

Introduction Let $p$ be a prime number.

Throughout, let $R$ be a commutative Noetherian local ring with maximal ideal $\mathfrak{m}$ and residue field $k=R/\mathfrak{m}$.

Let $K$ be an algebraically closed field of characteristic $0$.

Introduction The Riemann zeta function is widely known (to be the analytic continuation of Euler’s zeta function): It is widely known mainly because of the celebrated hypothesis by Riemann that remains unsolved after more than a century’s attempts by math…

Background in Basic Field Theory Let $K$ be a field (in this post we mostly assume that $K \supset \mathbb{Q}$) and $n$ an integer $>1$ which is not divisible by the characteristic of $K$.

Heights Definition.