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pro vyhledávání: '"11F80"'
We consider a special subsequence of the Fourier coefficients of powers of the Dedekind $\eta$-function, analogous to the sequence $\delta_\ell := 24^{-1} \pmod{\ell}$ on which exceptional congruences of the partition function are supported. Therefro
Externí odkaz:
http://arxiv.org/abs/2411.17638
Autor:
Loeffler, David, Zerbes, Sarah Livia
In our earlier work with Christopher Skinner (J. Eur. Math. Soc 24 (2022), no. 2; DOI 10.4171/JEMS/1124; Arxiv 1706.00201), we constructed Euler systems for the 4-dimensional spin Galois representations corresponding to automorphic forms for GSp(4).
Externí odkaz:
http://arxiv.org/abs/2411.12576
Autor:
Huryn, Jake, Zhang, Yifei
Let $X$ be a connected normal scheme of finite type over $\mathbf{Z}$, let $G$ be a connected reductive group over $\mathbf{Q}$, and let $\{\rho_\ell\colon\pi_1(X[1/\ell])\to G(\mathbf{Q}_\ell)\}_\ell$ be a Frobenius-compatible collection of continuo
Externí odkaz:
http://arxiv.org/abs/2411.08259
Autor:
van Bommel, Raymond, Costa, Edgar, Elkies, Noam D., Keller, Timo, Schiavone, Sam, Voight, John
We prove that the transitive permutation group 17T7, isomorphic to a split extension of $C_2$ by $\mathrm{PSL}_2(\mathbb{F}_{16})$, is a Galois group over the rationals. The group arises from the field of definition of the 2-torsion on an abelian fou
Externí odkaz:
http://arxiv.org/abs/2411.07857
Autor:
Zhang, Xiaoyu
Let $G$ be a definite special orthogonal group over a totally real number field $F$. The work of Arthur associates Galois representations to automorphic representations of $G(\mathbb{A}_F)$ under certain conditions. In this article, we apply the meth
Externí odkaz:
http://arxiv.org/abs/2411.04897
Autor:
Pham, Dat
In this short note, we give a new proof of a recent result of Tong Liu on torsions in the graded pieces of a Nygaard filtration associated to a crystalline lattice. Our approach is inspired on the one hand by a result of Gee--Kisin on the shape of mo
Externí odkaz:
http://arxiv.org/abs/2411.04069
Autor:
Čoupek, Pavel
Let $K$ be an absolutely unramified $p$-adic field. We establish a ramification bound, depending only on the given prime $p$ and an integer $i$, for mod $p$ Galois representations associated with Wach modules of height at most $i$. Using an instance
Externí odkaz:
http://arxiv.org/abs/2410.23453
We compute the conductor exponents at odd places using the machinery of cluster pictures of curves for three infinite families of hyperelliptic curves. These are families of Frey hyperelliptic curves constructed by Kraus and Darmon in the study of th
Externí odkaz:
http://arxiv.org/abs/2410.21134
Autor:
Kumar, Arvind, Mishra, Prabhat Kumar
Let $k \ge 2$ be an even integer, $ \ell \ge \max\{5, k-1\} $ be a prime, and $N$ be a squarefree positive integer. It is known that if the $\rm{mod}\,\ell$ Galois representation $\overline{\rho}_f$ associated with a newform $f$ of weight $k$, level
Externí odkaz:
http://arxiv.org/abs/2410.16854
Autor:
Merkurjev, Alexander, Scavia, Federico
For every finite group $H$ and every finite $H$-module $A$, we determine the subgroup of negligible classes in $H^2(H,A)$, in the sense of Serre, over fields with enough roots of unity. As a consequence, we show that for every odd prime $p$, every in
Externí odkaz:
http://arxiv.org/abs/2410.12560