Related papers: Indices of inseparability and refined ramification…

Given a linear group G over a field k, we define a notion of index and residue of an element g of G(k((t)). This provides an alternative proof of Gabber's theorem stating that G has no subgroups isomorphic to the additive or the commutative…

We continue generalizing Altu\u{g}'s work on $\mathsf{GL}_2$ over $\mathbb{Q}$ in the unramified setting for \emph{Beyond Endoscopy} to the ramified case where ramification occurs at $S=\{\infty,q_1,\dots,q_r\}$ with $2\in S$, after…

We describe the necessary and sufficient numerical condition when an element $X$ in the Picard group of $K(2)$-local category at prime $p \geqslant 5$ is of finite type, i.e., $\pi_kX$ is finitely generated as a $\mathbb{Z}_p$-module for…

Let $p$ be a prime number, let $K$ be a $p$-field (a local field with finite residue field of characteristic $p$), let $L$ be a finite galoisian tamely ramified extension of $K$, and let $G=\mathrm{Gal}(L|K)$. Suppose that $L$ is split over…

Let $p$ be a rational prime, let $F$ denote a finite, unramified extension of $\mathbb{Q}_p$, let $K$ be the completion of the maximal unramified extension of $\mathbb{Q}_p$, and let $\overline{K}$ be some fixed algebraic closure of $K$.…

Let $k$ be a complete nonarchimedean field and let $X$ be an affinoid closed disc over $k$. We classify the tamely ramified twisted forms of $X$. Generalizing work of P. Russell on inseparable forms of the affine line we construct explicit…

If $i:A\subset B$ is a commutative ring extension, we show that the group $\mathcal I(A,B)$ of invertible $A$-submodules of $B$ is contracted in the sense of Bass, with $L\mathcal I(A,B)=H^0_{et}(A,i_*\mathbb Z/\mathbb Z)$. This gives a…

We give a formula for the number of newforms in $S_k^{\mathrm{new}}(N)$ that have prescribed ramified supercuspidal components $\pi_p$ at a set $T$ of primes dividing $N$. This dimension is given in terms of the trace of the Atkin--Lehner…

We prove a general version of the "Stability Theorem": if $K$ is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions, and if $F|K$ is a finitely generated (transcendental) extension of…

Let $K$ be any finite extension of $Q_{p}$, $L$ any finite Galois extension of $K$ and $E$ any finite large enough coefficient field containing $L$. We classify two-dimensional, F-semistable $E$-representations of $G_{K}$, by listing the…

Let p be an odd prime, and k_\infty the cyclotomic Z_p-extension of an abelian field k. For a finite set S of rational primes which does not include p, we will consider the maximal S-ramified abelian pro-p extension M_S(k_\infty) over…

We study the exclusive rare decay B -> K l(bar) l. We calculate the relevant form factors within a relativistic constituent quark model, for the first time without employing the impulse approximation. The calculated form factors are used to…

Let $p$ be a prime number and let $K$ be a genus one two-bridge knot. In the spirit of arithmetic topology, we observe that if $p$ divides the size of the 1st homology group of some odd-th cyclic branched cover of the knot $K$, then its…

Let $F/K$ be a finite Galois totally & wildly ramified extension of complete discrete valuation fields. We say that the extension has the Hasse-Arf property if the ramification jumps in upper numbering are integers. We give necessary…

We find necessary and sufficient conditions for the finite separability of finitely generated commutative rings. Namely, we prove that every such ring is a finite extension of its torsion ideal $I_k$ where $k$ is square-free, and $I_k$ is a…

We prove the following result: Let B be a smooth, irreducible, quasi-projective variety over the complex numbers and assume that B has a projective compactification \bar{B} such that \bar{B} - B is of codimension at least two in \bar{B}.…

Let $A_p(\C)$ be the space of entire functions such that $| f(z)|\le Ae^{Bp(z)}$ for some $A,B>0$ and let $V$ be a discrete sequence of complex numbers which is not a uniqueness set for $A_p(\C)$. We use $L^2$ estimates for the…

Let K be a complete discrete valuation field of mixed characteristic (0,p) with algebraically closed residue field, and let f: Y --> P^1 be a three-point G-cover defined over K, where G has a cyclic p-Sylow subgroup P. We examine the stable…

Let $p$ be prime. Let $L/K$ be a finite, totally ramified, purely inseparable extension of local fields, $\left[ L:K\right] =p^{n},\;n\geq2.$ It is known that $L/K$ is Hopf Galois for numerous Hopf algebras $H,$ each of which can act on the…

Let p\in\{2,3\}, and let k be an imaginary quadratic field in which p decomposes into two distinct primes \mathfrak{p} and \bar{\mathfrak{p}}. Let k_\infty be the unique Z_p-extension of k which is unramified outside of \mathfrak{p}, and…