3 papers
math.NT2026
The commutative algebra of congruence ideals and applications to number theory
Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning
In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick…
math.NT2024
Mod multiplicities in certain Shimura varieties
Jeffrey Manning
We use the Taylor-Wiles-Kisin patching method to investigate the multiplicities with which Hecke eigensystems appear in the mod- cohomology of unitary Shimura sets, associate…
math.NT2024
Congruence modules and the Wiles-Lenstra-Diamond numerical criterion in higher codimensions
Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning
We define a congruence module associated to a surjective -algebra morphism , with a discrete valuation ring, a c…