Arithmetic properties of signed Selmer groups at non-ordinary primes
We extend many results on Selmer groups for elliptic curves and modular forms to the non-
ordinary setting. More precisely, we study the signed Selmer groups defined using the …
ordinary setting. More precisely, we study the signed Selmer groups defined using the …
Upper bounds for constant slope p-adic families of modular forms
J Bergdall - Selecta Mathematica, 2019 - Springer
We study p-adic families of eigenforms for which the p-th Hecke eigenvalue a_p ap has
constant p-adic valuation (“constant slope families”). We prove two separate upper bounds …
constant p-adic valuation (“constant slope families”). We prove two separate upper bounds …
Limiting measures of supersingularities
B Arsovski - arXiv preprint arXiv:1911.12220, 2019 - arxiv.org
Let $ p $ be a prime number and let $ k\geq 2$ be an integer. In this article we study the
semi-simple reductions modulo $ p $ of two-dimensional irreducible crystalline $ p $-adic …
semi-simple reductions modulo $ p $ of two-dimensional irreducible crystalline $ p $-adic …
A zig-zag conjecture and local constancy for Galois representations
E Ghate - arXiv preprint arXiv:1903.08996, 2019 - arxiv.org
We make a zig-zag conjecture describing the reductions of irreducible crystalline two-
dimensional representations of $ G_ {{\mathbb {Q}} _p} $ of half-integral slopes and …
dimensional representations of $ G_ {{\mathbb {Q}} _p} $ of half-integral slopes and …
Reductions of Galois representations of Slope
E Ghate, V Rai - arXiv preprint arXiv:1901.01728, 2019 - arxiv.org
We prove a zig-zag conjecture describing the reductions of irreducible crystalline two-
dimensional representations of $ G_ {{\mathbb {Q}} _p} $ of slope $\frac {3}{2} $ and …
dimensional representations of $ G_ {{\mathbb {Q}} _p} $ of slope $\frac {3}{2} $ and …