181 citations · 368 across the 15 of their papers we have counts for
19 papers
Corrigendum to "Stability in the high-dimensional cohomology of congruence subgroups" [Compos. Math. 156 (2020), no. 4, 822-861]
Jeremy Miller, Rohit Nagpal, Peter Patzt
After the publication of [Compos. Math. 156 (2020), no. 4, 822-861], Andrew Putman pointed out a mistake in our paper and helped us fix it. In this note, we will explain what this…
Symmetric modules over the infinite polynomial ring I: nilpotent quotients
Rohit Nagpal, Andrew Snowden, Teresa Yu
Cohen proved that the infinite variable polynomial ring is noetherian with respect to the action of the infinite symmetric group . The first two…
Symmetric ideals of the infinite polynomial ring
Rohit Nagpal, Andrew Snowden
Let be the infinite variable polynomial ring, equipped with the natural action of the infinite symmetric group . We classify the $\math…
On the geometry and representation theory of isomeric matrices
Rohit Nagpal, Steven V Sam, Andrew Snowden
The space of complex matrices can be regarded as an algebraic variety on which the group acts. There is a rich interaction between geome…
Symmetric subvarieties of infinite affine space
Rohit Nagpal, Andrew Snowden
We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these va…
Periodicity in the cohomology of finite general linear groups via q-divided powers
Rohit Nagpal, Steven V Sam, Andrew Snowden
We show that canonically admits the structure of a module over the -divided power algebra (assuming …
The semi-linear representation theory of the infinite symmetric group
Rohit Nagpal, Andrew Snowden
We study the category of smooth semilinear representations of the infinite symmetric group over the field of rational functions in infinitely many variables. We estab…
VI modules in non-describing characteristic, Part II
Rohit Nagpal
We classify all irreducible generic -modules in non-describing characteristic. Our result degenerates to yield a classification of irreducible generic -mo…
Stability in the high-dimensional cohomology of congruence subgroups
Jeremy Miller, Rohit Nagpal, Peter Patzt
We prove a representation stability result for the codimension-one cohomology of the level three congruence subgroup of . This is a special case of a que…
modules in non-describing characteristic, Part I
Rohit Nagpal
Let be the category of finite dimensional -vector spaces whose morphisms are injective linear maps, and let be a noetherian ring. We study…
Linear and quadratic ranges in representation stability
Thomas Church, Jeremy Miller, Rohit Nagpal +1
We prove two general results concerning spectral sequences of -modules. These results can be used to significantly improve stable ranges in a large portion of the stab…
Periodicity in the cohomology of symmetric groups via divided powers
Rohit Nagpal, Andrew Snowden
A famous theorem of Nakaoka asserts that the cohomology of the symmetric group stabilizes. The first author generalized this theorem to non-trivial coefficient systems, in the form…
Regularity of FI-modules and local cohomology
Rohit Nagpal, Steven V Sam, Andrew Snowden
We resolve a conjecture of Li and Ramos that relates the regularity of an FI-module to its local cohomology groups. This is an analogue of the familiar relationship between regular…
Noetherianity of some degree two twisted skew-commutative algebras
Rohit Nagpal, Steven V Sam, Andrew Snowden
A major open problem in the theory of twisted commutative algebras (tca's) is proving noetherianity of finitely generated tca's. For bounded tca's this is easy, in the unbounded ca…
Gröbner coherent rings and modules
Rohit Nagpal, Andrew Snowden
Let be a graded ring. We introduce a class of graded -modules called Gröbner-coherent modules. Roughly, these are graded -modules that are coherent as ungraded modules be…
The module theory of divided power algebras
Rohit Nagpal, Andrew Snowden
We study modules for the divided power algebra in a single variable over a commutative noetherian ring . Our first result states that is a coherent ring. In fact, we sho…
FI-modules and the cohomology of modular representations of symmetric groups
Rohit Nagpal
An FI-module over a commutative ring encodes a sequence of representations of the symmetric groups over . In t…
Noetherianity of some degree two twisted commutative algebras
Rohit Nagpal, Steven V Sam, Andrew Snowden
In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we…
FI-modules over Noetherian rings
Thomas Church, Jordan S. Ellenberg, Benson Farb +1
FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an…