Jack Hall
Assistant Professor

email: firstnamelastname at math dot arizona dot edu
office: ENR2 S349
phone: +1 520-621-0729
interests: moduli spaces, algebraic stacks, derived categories, formal geometry, and deformation theory.
seminar: homepage
arXiv: listings
orcid-id: 0000-0001-9136-7059

#### Publications

• A Luna étale slice theorem for algebraic stacks (with J. Alper and D. Rydh)
Annals of Mathematics, to appear pdf

• Coherent Tannaka duality and algebraicity of Hom-stacks (with D. Rydh)
Algebra & Number Theory, Volume 13 (2019), Issue 7, 1633-1675 journal pdf

• Artin's criteria for algebraicity revisited (with D. Rydh)
Algebra & Number Theory, Volume 13 (2019), Issue 4, 749-796 journal pdf

• One positive and two negative results for derived categories of algebraic stacks (with A. Neeman and D. Rydh)
Journal of the Institute of Mathematics of Jussieu, Volume 18, Issue 5, September 2019, pp. 1087-1111 journal pdf

• Addendum to "Étale dévissage, descent and pushouts of stacks" [J. Algebra 331 (1) (2011) 194-223] (with D. Rydh)
Journal of Algebra, Volume 498, 15 March 2018, Pages 398-412 journal pdf

• Perfect complexes on algebraic stacks (with D. Rydh)
Compositio Mathematica, Volume 153, Issue 11, November 2017, pp. 2318-2367 journal pdf

• The telescope conjecture for algebraic stacks (with D. Rydh)
Journal of Topology, Volume 10, Issue 3, September 2017, pages 776-794 journal pdf

• Openness of versality via coherent functors
Journal für die reine und angewandte Mathematik (Crelle's Journal), Volume 2017, Issue 722, Pages 137-182 journal pdf

• The Balmer spectrum of a tame stack
Annals of K-Theory, Volume 1 (2016), Issue 3, 259-274 journal pdf

• Algebraic groups and compact generation of their derived categories of representations (with D. Rydh)
Indiana University Mathematics Journal, Volume 64, Issue 6, 2015, pp. 1903-1923 journal pdf

• General Hilbert and Quot stacks (with D. Rydh)
Michigan Mathematical Journal, Volume 64, Issue 2 (2015), 335-347 journal pdf

• Cohomology and base change for algebraic stacks
Mathematische Zeitschrift, October 2014, Volume 278, Issue 1-2, pp 401-429 journal pdf

• A relative GAGA principle for families of curves
Journal of the London Mathematical Society (2014), Volume 90, Issue 1, Pp. 29-48 journal pdf

• The Hilbert Stack (with D. Rydh)
Advances in Mathematics, Volume 253, 1 March 2014, Pages 194-233 journal pdf

• The moduli stack of (all) curves
Appendix B to: Towards a classification of modular compactifications $\mathcal{M}_{g,n}$
Inventiones Mathematicae, May 2013, Volume 192, Issue 2, pp 459-503 journal pdf

• The étale local structure of algebraic stacks (with J. Alper and D. Rydh)
Submitted pdf

• Mayer-Vietoris squares in algebraic geometry (with D. Rydh)
Submitted pdf

• GAGA theorems
Submitted pdf

• Tannaka duality for algebraic stacks with quasi-affine diagonal (with D. Rydh)
In preparation

• Coherence criteria for half-exact functors (with D. Rydh)
In preparation

#### Past Teaching

MATH 313: Introduction to linear algebra (Fall 2019), sections 1 and 2
MATH 536B: Algebraic Geometry (Spring 2019)
MATH 129: Calculus II (Fall 2018), sections 3 and 5
MATH 511B: Algebra (Spring 2018)
MATH 511A: Algebra (Fall 2017)
MATH 536B: Algebraic Geometry (Spring 2017)
MATH 536A: Algebraic Geometry (Fall 2016)