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5 papers · 1 filter
Resolutions of spaces of crystalline representations and modularity
Robin Bartlett, Bao V. Le Hung, Brandon Levin
We introduce a new partial resolution of crystalline spaces of Galois representations when the gaps in Hodge--Tate weights are smaller than , with no bound on ramification. Furt…
Galois representation of the product of two Drinfeld modules of generic characteristic
Lian Duan, Jiangxue Fang
In this paper, we study the Galois representations attached to products of Drinfeld modules. As a function-field analogue of Serre's classical open image theorem for products of el…
On the Quadratic Structure of Torsors over Affine Group Schemes
Philippe Cassou-Noguès, Martin J. Taylor
Let be a finite and flat group scheme over the ring of algebraic integers of a number field and suppose that the generic fiber of $\mathcal{G…
Parity of the partition function in quadratic progressions
Ken Ono, Ashvin Swaminathan
The parity of the partition function is one of the most stubborn problems in number theory. In 2010, the first author conjectured, for square-free , t…
The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one
Sunil K. Chebolu, Ján Mináč, Cihan Okay +2
The famous Bloch--Kato conjecture implies that for a field containing a primitive th root of unity, the cohomology ring of the absolute Galois group of with $\math…