4 problems

Let $F$ be the field and $G$ the group occurring above, let $\theta$, $\boldsymbol{\textstyle\bigwedge}^1_{\mathbb{C}_p[G]}$ and $\boldsymbol{e}_\chi$ be as defined in the surround…

Let $F$ be the number field, $M$ the motive, and $A$ the coefficient algebra under consideration. Write $M^{\ast}(1)$ for the dual Tate twist, $H^i(F,-)$ for global cohomology,…

Chinburg's conjecture. If $G$ has no irreducible symplectic representation, then

Fix a prime number $\ell$, let $S$ contain $\ell$, $\infty$, and the primes ramified in $F$, put $A_\ell=A\otimes_{\mathbb{Q}}\mathbb{Q}_\ell$, and let … be the isomorphism induced…