# 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

### Professional Information:

My CV and Publications (most of these are available below)

### Teaching:

I am on sabbatical academic year 2015-2016.

### Papers:

My research is partially funded by NSF grant DMS-1303173 and a grant from The Simons Foundation (for 2015-2016 I am a Simons Fellow). 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.

• 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.pdf.

• 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.

• 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:

• Algebraic spaces and stacks (graduate level textbook).
• 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