# Martin Olsson

### Contact me:

The best way to reach me is to email me at
martinolsson[at]university-name[dot]edu (my old math account also forwards all mail here), stop by my office Evans 879.

Mail can also be sent to:
Martin Olsson

Department of Mathematics

970 Evans Hall #3840

University of California

Berkeley, CA 94720-3840

### Papers:

My research is partially funded by NSF grant DMS-1902251.
The versions of my papers below often differ (sometimes substantially) from the final published version. For purposes of citation please refer to the published version.
A complete list of my papers (as well as links to the published versions) can be found in Mathscinet.
The Zariski topology, linear systems, and algebraic varieties pdf, with János Kollár, Max Lieblich, and Will Sawin.
Gluing complexes in a D-topos pdf
Representability of cohomology of finite flat abelian group schemes arxiv link With Daniel Bragg.
Deformation theory of perfect complexes and traces arxiv link With Max Lieblich.
Theta functions for monomial degenerations pdf
Derived categories and birationality arxiv link. With Max Lieblich
Points with large stabilizer groups and sections of vector bundles pdf.
Topological reconstruction theorems for varieties arxiv link. With János Kollár, Max Lieblich, and Will Sawin.
A geometric construction of semistable extensions of crystalline representations pdf.
Kummer coverings and specialization pdf
Finiteness of etale fundamental groups by reduction modulo p arxiv link With Bhargav Bhatt and Ofer Gabber
A stronger derived Torelli theorem for K3 surfaces pdf. With Max Lieblich
Independence of l and traces on cohomology pdf.
Sheaves on curves and their local terms pdf.
l-derived schemes and local terms pdf.
Compatible systems and correspondences pdf.
Motivic cohomology, localized Chern classes, and local terms pdf. To appear in Manuscripta Math.
Borel-Moore homology, Riemann-Roch transformations, and local terms pdf, Advances in Math. 273 (2015), 56-123.
The earlier preprint "Localized Chern classes and independence of l" was revised and divided into the preceding two papers.
Moduli of spherical varieties and log geometry pdf. To appear in Algebraic Geometry.
Fourier-Mukai partners of K3 surfaces in positive characteristic pdf, with Max Lieblich. To appear in Annales scientifique de l'ENS.
Compactifications of moduli of abelian varieties: An introduction pdf in "Current Developments in Algebraic Geometry", 295–348, Math. Sci. Res. Inst. Publ., 59, Cambridge Univ. Press, Cambridge, 2012.
Logarithmic geometry and moduli pdf, with Abramovich, Chen, Gillam, Huang, Satriano, and Sun. To appear in Handbook of Moduli, Farkas and Morrison eds.
Independence of $\ell $ and surfaces pdf, with P. Mannisto.
Nagata compactification for algebraic spaces pdf. With Brian Conrad and Max Lieblich. J. Inst. Math. Jussieu 11 (2012), 747–814.
The bar construction and affine stacks pdf. To appear in Communications in Algebra.
Integral models for moduli spaces of G-torsors pdf. Annales de l'institut Fourier 62 (2012), 1483-1549.
Twisted stable maps to tame Artin stacks pdf. With D. Abramovich and A. Vistoli. J. Algebraic Geom. 20 (2011), 399–477.
Fujiwara's theorem for equivariant correspondences pdf. J. Algebraic Geometry 24 (2015), 401-497.
Logarithmic interpretation of the main component in toric Hilbert schemes, in Proceedings of the International Conference on Curves and Abelian Varieties
Edited by: Valery Alexeev, Arnaud Beauville, Herb Clemens, and Elham Izadi. pdf.
The Picard group of $M_{1,1}$ pdf, dvi. With William Fulton. Algebra and Number Theory 4 (2010), 87-104.
Tame stacks in positive characteristic, With Dan Abramovich and Angelo Vistoli. Anneles de l'Institut Fourier 58 (2008), 1057-1091. pdf.
Generators and relations for the etale fundamental group pdf, dvi, With Max Lieblich. Pure and Applied Math Quarterly 6 (2010), 209-244.
Canonical compactifications of moduli spaces for abelian varieties. Chapters 3 and 4 of this monograph contain the results of my earlier preprint "Modular description of the main components in Alexeev's compactifications". Springer Lecture Notes in Math 1958. pdf.
Perverse sheaves on Artin stacks, With Yves Laszlo. Math. Zeit. 261, (2009), 737-748. pdf
The six operations for sheaves on Artin stacks II: adic coefficients
. With Yves Laszlo. Publ. Math. IHES 107 (2008), 169-210. pdf.
On Faltings' method of almost \'etale extensions pdf Algebraic geometry---Seattle 2005, Part 2, 811--936, Proc. Sympos. Pure Math. 80, Part 2, Amer. Math. Soc., Providence, RI, 2009.
The six operations for sheaves on Artin stacks I: finite coefficients. With Yves Laszlo. Publ. Math. IHES 107 (2008), 109--168. pdf.
On the global quotient structure of the space of twisted stable maps to a quotient stack. With D. Abramovich, T. Graber, and H.-H. Tseng. Journal of Algebraic Geometry 16 (2007), 731-751.pdf.
On (log) twisted curves. Comp. Math. 143 (2007), 476-494. pdf.
Hom--stacks and restriction of scalars. Duke Math. J. 134 (2006), 139-164. pdf.
A boundedness theorem for Hom-stacks. Mathematical Research Letters 14 (2007), 1009-1023. pdf.
Crystalline cohomology of algebraic stacks and Hyodo-Kato cohomology
. Asterisque 316.
Sheaves on Artin stacks
. J. Reine Angew. Math. (Crelle's Journal) 603 (2007), 55-112.pdf.
Towards non--abelian $P$--adic Hodge theory in the good reduction
case pdf. Memoirs of the AMS 210 (2011).
F-isocrystals and homotopy types,
J. Pure and Applied Algebra 210 (2007), 591-638. pdf.
On proper coverings of Artin stacks,
Advances
in Mathematics 198 (2005), 93-106.
A stacky semi-stable reduction theorem
, Int. Math. Res. Not.
29 (2004), 1497--1509.pdf.

Kawamata-Viehweg vanishing as Kodaira vanishing for stacks
.
with Kenji Matsuki. Math. Res. Letters 12 (2005), 207-217. pdf.

The logarithmic cotangent complex.
Math. Ann. 333, 859--931 (2005)

Deformation theory of representable morphisms of algebraic stacks.
Math. Zeit. 253 (2006), 25-62.

Logarithmic geometry and algebraic stacks.
Ann. Sci. d'ENS 36 (2003), 747--791.pdf.

Universal log structures on semi-stable varieties.
Tohoku Math Journal 55 (2003) 397--438.pdf.

Semi-stable degenerations and period spaces for polarized K3 surfaces.
Duke Math. J. 125 (2004), 121-203.pdf. Erratum

Quot functors for Deligne-Mumford stacks.
with Jason Starr. Special volume in honor
of S. Kleiman's 60th birthday, Comm. Alg. 31 (2003) 4069--4096.pdf.

Log algebraic stacks and moduli of log schemes (my thesis)
dvi, ps.

### Expository:

Exercises for my lectures for the Berkeley-Tokyo Lectures on Number Theory. Exercises for lecture 1, Exercises for lecture 2.
Algebraic spaces and stacks (graduate level textbook). Colloquium Publications 62, American Mathematical Society (2016). Errata and further comments.
Lecture notes from my lectures at MSRI during the workshop on deformation theory and moduli in algebraic geometry (July 23-August 3, 2007), pdf.
Lecture notes for three talks on abelian varieties I gave at a workshop in Hangzhou, China (August, 2009): Notes