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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

6 votes
Accepted

Number of homomorphism, or number of solution to equations, in finite groups

There are $70$ homomorphisms from $\mathbb{Z}\times\mathbb{Z}$ to the dihedral group of order $14$.
Jeremy Rickard's user avatar
13 votes

Bass' stable range of $\mathbf Z[X]$

There's a comment at the top of page 993 of L N Vaseršteĭn, A A Suslin, "Serre's problem on projective modules over polynomial rings, and algebraic K-theory", Math. USSR Izv., 1976, 10 (5), 937–1001, …
Jeremy Rickard's user avatar
5 votes
Accepted

Periods in the trivial extension algebra of the incidence algebra of the divisor lattice

Calculating periods of simple modules for the trivial extension algebra $TA$ can be reduced to a calculation with $A$-modules (at least if $A$ has finite global dimension), which is much easier. The …
Jeremy Rickard's user avatar
13 votes
Accepted

Can we glue characteristic 0 and characteristic p representations of a finite group given eq...

The condition on Brauer characters is not sufficient. Let $G$ be a $p$-group, $\pi$ any nontrivial representation over $\mathbb{F}_p$, and $\sigma$ the trivial representation over $\mathbb{Q}_p$ of t …
Jeremy Rickard's user avatar
5 votes

A question on bi-character of finite abelian group

You can choose integers $m_1,m_2,n_1,n_2$ so that $m_1$ and $n_1$ are coprime to $p$ and $m_2$ and $n_2$ are coprime to $q$, and such that $n_1m_2b(a_1,b_2)=0=n_2m_1b(a_2,b_1)$. Then $$b(n_1a_1+n_2a_2 …
Jeremy Rickard's user avatar