Speaker: Anwesh Ray
Affiliation: CMI, Chennai
Title: Galois representations ramified at one prime
Date and Time: February 14, 2024, 14:30:00 Hours
Venue: AG-77
Asbtract: Given any prime $p\geq 7$ and a natural number $n>1$, we construct global Galois representations with large image in $GL_n(\mathbb{Z}_p)$ that are unramified outside $\{p\}$. This improves upon a result of Greenberg, who constructed such representations for regular primes $p$ and natural numbers $n$ such that $p\geq 4\lfloor n/2\rfloor+1$. The results are proven via an application of Galois deformation theory, a technique that is used to lift mod-$p$ Galois representations to characteristic zero $p$-adic rings.
Affiliation: CMI, Chennai
Title: Galois representations ramified at one prime
Date and Time: February 14, 2024, 14:30:00 Hours
Venue: AG-77
Asbtract: Given any prime $p\geq 7$ and a natural number $n>1$, we construct global Galois representations with large image in $GL_n(\mathbb{Z}_p)$ that are unramified outside $\{p\}$. This improves upon a result of Greenberg, who constructed such representations for regular primes $p$ and natural numbers $n$ such that $p\geq 4\lfloor n/2\rfloor+1$. The results are proven via an application of Galois deformation theory, a technique that is used to lift mod-$p$ Galois representations to characteristic zero $p$-adic rings.