相关论文: Toward Abhyankar's Inertia Conjecture for PSL_2(\e…

In this paper, we utilize our previous results on mod p monodromy of cyclic coverings of the projective line to realize a large series of groups of the form PSL(n, q) and PSU(n, q) as Galois groups over Q. We achieve for the first time a…

We establish non-unirational versions of Hilbert Irreducibility for all Hilbert modular surfaces which are of K3 type. As an application we prove new instances of the regular Inverse Galois Problem for the simple groups…

Let $p$ and $q$ be odd prime numbers. In this paper we study non-abelian pq-fold regular covers of the projective line, determine algebraic models for some special cases and provide a general isogeny decomposition of the corresponding…

For any odd prime $p,$ we construct an infinite family of pairs of imaginary quadratic fields $\mathbb{Q}(\sqrt{d}),\mathbb{Q}(\sqrt{d+1})$ whose class numbers are both divisible by $p.$ One of our theorems settles Iizuka's conjecture for…

We show that for all odd primes $p$, there exist ordinary elliptic curves over $\bar{\mathbb{F}}_p(x)$ with arbitrarily high rank and constant $j$-invariant. This shows in particular that there are elliptic curves with arbitrarily high rank…

Let p be an odd prime number. Using some previous work of the two authors, we determine the socle filtration of all irreducible smooth mod p representations of SL(2,Q_{p}).

We construct infinite families of irreducible supersingular mod $p$ representations of $\mathrm{GL}_2(F)$ with $\mathrm{GL}_2(\mathcal{O}_F)$-socle compatible with Serre's modularity conjecture, where $F / \mathbb{Q}_p$ is any finite…

We prove a pro-$p$ version of Sela's theorem stating that a finitely generated group is $k$-acylindrically accessible. This result is then used to prove that $\mathrm{PD}^n$ pro-$p$ groups admit a unique $k$-acylindrical JSJ-decomposition.

We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show that the data in the "basic construction" of genus 2 covers of…

In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the Galois group of some finite extension…

We study the $p$-rank stratification of the moduli space of Prym varieties in characteristic $p > 0$. For arbitrary primes $p$ and $\ell$ with $\ell \not = p$ and integers $g \geq 3$ and $0 \leq f \leq g$, the first theorem generalizes a…

We decompose the restriction of ramified principal series representations of the $p$-adic group $\mathrm{GL}(3,\mathrm{k})$ to its maximal compact subgroup $K=\mathrm{GL}(3,\mathscr{R})$. Its decomposition is dependent on the degree of…

Let $p$ be a fixed odd prime and let $K$ be an imaginary quadratic field in which $p$ splits. Let $A$ be an abelian variety defined over $K$ with supersingular reduction at both primes above $p$ in $K$. Under certain assumptions, we give a…

We prove that in the function field setting, $\ell$-torsion in the class groups of quadratic fields can be arbitrarily large. In fact, we explicitly produce a family whose $\ell$-rank growth matches the growth in the setting of genus…

We present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups. These bundles are akin to those of Fadell-Neuwirth for configuration spaces, and their existence is detected by a…

Let $\ell$ be a prime number, $k$ a positive integer and consider the group $\Gamma_{\ell^k} :=\langle a,b\ \vert\ a^{\ell^k(\ell^k-1)}ba^{-\ell^k}b^{-2}\rangle$. We prove that $\Gamma_{\ell^k}$ is not $\mathrm{SL}_2$-weakly integral with…

We study embeddings of $\mathrm{PSL}_2(p^a)$ into exceptional groups $G(p^b)$ for $G=F_4,E_6,{}^2\!E_6,E_7$, and $p$ a prime with $a,b$ positive integers. With a few possible exceptions, we prove that any almost simple group with socle…

Atiyah and Hirzebruch gave examples ofeven degree torsion classes in the singularcohomology of a smooth complex projective manifold, which arenot Poincar\'{e} dual to an algebraiccycle. We notice that the order ofthese classes are small…

We prove the density hypothesis for congruence subgroups of an irreducible uniform lattice in $\mathrm{PSL}_2(\mathbb{R})^d$, extending previous results on the spherical density hypothesis to bound multiplicities of non-tempered…

In this paper, we prove that a \(p\)-block with abelian defect group is inertial if it covers a \(p\)-block of a normal subgroup of \(p\)-power index having only one irreducible Brauer character orbit.