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pro vyhledávání: '"Kramer, Kenneth P."'
Autor:
Brumer, Armand, Kramer, Kenneth
We say that an abelian variety $A_{/\mathbb{Q}}$ of dimension $g$ is prosaic if it is semistable and its points of order $2$ generate a $2$-extension of $\mathbb{Q}$. We focus on prosaic abelian varieties $A$ with good reduction outside one prime $p$
Externí odkaz:
http://arxiv.org/abs/2305.11026
Autor:
Brumer, Armand, Kramer, Kenneth
An abelian threefold $A_{/{\mathbb Q}}$ of prime conductor $N$ is favorable if its 2-division field $F$ is an ${\mathcal S}_7$-extension over ${\mathbb Q}$ with ramification index 7 over ${\mathbb Q}_2$. Let $A$ be favorable and let $B$ be a semistab
Externí odkaz:
http://arxiv.org/abs/2002.00510
Akademický článek
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Akademický článek
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Autor:
Brumer, Armand, Kramer, Kenneth
Motivated by our arithmetic applications, we required some tools that might be of independent interest. Let $\mathcal E$ be an absolutely irreducible group scheme of rank $p^4$ over $\mathbb Z_p$. We provide a complete description of the Honda system
Externí odkaz:
http://arxiv.org/abs/1701.01890
Autor:
Brumer, Armand, Kramer, Kenneth
Publikováno v:
Alg. Number Th. 12 (2018) 1027-1071
An abelian surface $A_{/{\mathbb Q}}$ of prime conductor $N$ is favorable if its 2-division field $F$ is an ${\mathcal S}_5$-extension with ramification index 5 over ${\mathbb Q}_2$. Let $A$ be favorable and let $B$ be any semistable abelian variety
Externí odkaz:
http://arxiv.org/abs/1510.06249
We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform \pi_0 we prove an exact relation between the p-adic
Externí odkaz:
http://arxiv.org/abs/1302.2381
Autor:
Brumer, Armand, Kramer, Kenneth
We study the arithmetic of division fields of semistable abelian varieties A over the rationals. The Galois group of the 2-division field of A is analyzed when the conductor is odd and squarefree. The irreducible semistable mod 2 representations of s
Externí odkaz:
http://arxiv.org/abs/1102.4557
Autor:
Brumer, Armand, Kramer, Kenneth
A precise and testable modularity conjecture for rational abelian surfaces A with trivial endomorphisms, End_Q A = Z, is presented. It is consistent with our examples, our non-existence results and recent work of C. Poor and D. S. Yuen on weight 2 Si
Externí odkaz:
http://arxiv.org/abs/1004.4699
Autor:
Brumer, Armand, Kramer, Kenneth
Let $A$ be a semistable abelian variety defined over ${\bf Q}$ with bad reduction only at one prime $p$. Let $L= {\bf Q}(A[\ell])$ be the $\ell$-division field of $A$ for a prime $\ell$ not equal to $p$ and let $F={\bf Q}(\mu_\ell)$ be the cyclotomic
Externí odkaz:
http://arxiv.org/abs/math/0207309