PreprintarXiv licencearXiv
Grothendieck Pairs, Functors and Profinite Invariants
Abstract
As another variation of profinite properties, we define the notion of natural profinite invariants: functorial invariants, inducing isomorphisms for every Grothendieck pair. We give a characterisation of when adjoint functors are natural profinite invariants and describe a strategy on how to disprove natural profinite invariance. By means of examples we show that the notions of profinite invariance and natural profinite invariances are logically independent.
Related
- Grothendieck ring of varieties and at-the-characteristic numerical invariants
- Demailly-Kollár continuity on klt pairs, and applications to alpha and delta invariants
- Regularity of profinite isomorphisms of hyperbolic 3-manifolds
- Polycyclic groups and profinite isomorphism
- An algebro-geometric approach to profinite iterated monodromy groups
BibTeX
@misc{echtler2026grothendieck,
title = {{Grothendieck Pairs, Functors and Profinite Invariants}},
author = {Daniel Echtler},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38991},
eprint = {2610.38991},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38991},
}
RIS
TY - UNPB
TI - Grothendieck Pairs, Functors and Profinite Invariants
AU - Daniel Echtler
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38991
UR - https://arxiv.org/abs/2610.38991
AB - As another variation of profinite properties, we define the notion of natural profinite invariants: functorial invariants, inducing isomorphisms for every Grothendieck pair. We give a characterisation of when adjoint functors are natural profinite invariants and describe a strategy on how to disprove natural profinite invariance. By means of examples we show that the notions of profinite invariance and natural profinite invariances are logically independent.
ER -