8 citations · 22 across the 13 of their papers we have counts for
4 papers · 1 filter
Quantitative level lowering for Galois representations
Najmuddin Fakhruddin, Chandrashekhar Khare, Ravi Ramakrishna
We use Galois cohomology methods to produce optimal mod level lowering congruences to a -adic Galois representation that we construct as a well chosen lift of a given resi…
On the Shafarevich Group of Restricted Ramification Extensions of Number Fields in the Tame Case
Farshid Hajir, Christian Maire, Ravi Ramakrishna
Let be a number field and a finite set of places of . We study the kernels $\Sha_S$ of maps $H^2(G_S,\fq_p) \rightarrow \oplus_{v\in S} H^2(\G_v,\fq_p)$. There is a natu…
Infinite class field towers of number fields of prime power discriminant
Farshid Hajir, Christian Maire, Ravi Ramakrishna
For every prime number p, we show the existence of a solvable number field L ramified only at {p and infinity whose p-Hilbert Class field tower is infinite.
Cutting towers of number fields
Farshid Hajir, Christian Maire, Ravi Ramakrishna
Given a prime , a number field $\K$ and a finite set of places of $\K$, let $\K_S$ be the maximal pro- extension of $\K$ unramified outside . Using the Golod-Shafarevi…