3 citations · 16 across the 24 of their papers we have counts for
26 papers
The importance of being isolated
Scott Balchin, Juan Omar Gómez, Greg Stevenson
We give both a sufficient condition for and an obstruction to the derived category of a commutative ring being generated by its residue fields. As an illustration, we exhibit a rin…
Torsion models for tensor-triangulated categories
Scott Balchin, J. P. C. Greenlees, Luca Pol +1
Given a rigidly-compactly generated tensor-triangulated category whose Balmer spectrum is finite dimensional and Noetherian, we construct a torsion model for it, which is equivalen…
Classifying smashing ideals in derived categories of valuation domains
Scott Balchin, Florian Tecklenburg
Building on results of Bazzoni-Šťov\'ıček, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. In p…
Profinite equivariant spectra and their tensor-triangular geometry
Scott Balchin, David Barnes, Tobias Barthel
We study the tensor-triangular geometry of the category of equivariant -spectra for a profinite group, . Our starting point is the construction of a ``continu…
Prismatic decompositions and rational -spectra
Scott Balchin, Tobias Barthel, J. P. C. Greenlees
We study the tensor-triangular geometry of the category of rational -spectra for a compact Lie group . In particular, we prove that this category can be naturally decomposed…
Tensor-triangular rigidity in chromatic homotopy theory
Scott Balchin, Constanze Roitzheim, Jordan Williamson
We study the uniqueness of enhancements of tensor-triangulated categories. To do so, we provide conditions under which these enhancements interact well with categorical decompositi…
The combinatorics of operads for and
Scott Balchin, Ethan MacBrough, Kyle Ormsby
We provide a general recursive method for constructing transfer systems on finite lattices. Using this we calculate the number of homotopically distinct operads for dihe…
Lifting operads from conjugacy data
Scott Balchin, Ethan MacBrough, Kyle Ormsby
We isolate a class of groups -- called lossless groups -- for which homotopy classes of - operads are in bijection with certain restricted transfer systems on the pose…
Composition closed premodel structures and the Kreweras lattice
Scott Balchin, Ethan MacBrough, Kyle Ormsby
We investigate the rich combinatorial structure of premodel structures on finite lattices whose weak equivalences are closed under composition. We prove that there is a natural ref…
Big categories, big spectra
Scott Balchin, Greg Stevenson
We introduce a new topological invariant of a rigidly-compactly generated tensor-triangulated category and two new notions of support. The first is based on smashing subcategories:…
Model structures on finite total orders
Scott Balchin, Kyle Ormsby, Angélica M. Osorno +1
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order , we enume…
Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories
Scott Balchin, J. P. C. Greenlees
We prove the existence of various adelic-style models for rigidly small-generated tensor-triangulated categories whose Balmer spectrum is a one-dimensional Noetherian topological s…
Torsion models for tensor-triangulated categories: the one-step case
Scott Balchin, J. P. C. Greenlees, Luca Pol +1
Given a suitable stable monoidal model category and a specialization closed subset of its Balmer spectrum one can produce a Tate square for decomposing objects in…
Equivariant homotopy commutativity for
Scott Balchin, Daniel Bearup, Clelia Pech +1
We investigate the combinatorial data arising from the classification of equivariant homotopy commutativity for cyclic groups of order for distinct pri…
On the number of rational points of classifying stacks for Chevalley group schemes
Scott Balchin, Frank Neumann
We compute the number of rational points of classifying stacks of Chevalley group schemes using the Lefschetz-Grothendieck trace formula of Behrend for -adic cohomology of al…
-operads and associahedra
Scott Balchin, David Barnes, Constanze Roitzheim
We provide a new combinatorial approach to studying the collection of N-infinity-operads in G-equivariant homotopy theory for G a finite cyclic group. In particular, we show that f…
Adelic models of tensor-triangulated categories
J. P. C. Greenlees, Scott Balchin
We show that a well behaved Noetherian, finite dimensional, stable, monoidal model category is equivalent to a model built from categories of modules over completed rings in an ade…
Bousfield localisation and colocalisation of one-dimensional model structures
Scott Balchin, Richard Garner
We give an account of Bousfield localisation and colocalisation for one-dimensional model categories---ones enriched over the model category of -types. A distinguishing feature…
Augmented Homotopical Algebraic Geometry
Scott Balchin
We develop the framework for augmented homotopical algebraic geometry. This is an extension of homotopical algebraic geometry, which itself is a homotopification of classical algeb…
A Computational Method for Large Scale Searching of Counterexamples to the Strong Coincidence Conjecture
Scott Balchin
In this short note we report on results on a computational search for a counterexample to the strong coincidence conjecture. In particular, we discuss the method used so that furth…
Computations for symbolic substitutions
Dan Rust, Scott Balchin
We provide a survey of results from symbolic dynamics and algebraic topology relating to Grout, a new user-friendly program developed to calculate combinatorial properties and topo…
Homotopy of Planar Lie Group Equivariant Presheaves
Scott Balchin
We utilise the theory of crossed simplicial groups to introduce a collection of local Quillen model structures on the category of simplicial presheaves with a compact planar Lie gr…
Crossed Simplicial Group Categorical Nerves
Scott Balchin
We extend the notion of the nerve of a category for a small class of crossed simplicial groups, explicitly describing them using generators and relations. We do this by first consi…
Grout: A 1-Dimensional Substitution Tiling Space Program
Scott Balchin, Dan Rust
We introduce a GUI fronted program that can compute combinatorial properties and topological invariants of recognisable and primitive symbolic substitutions on finite alphabets and…