J.P. Pridham

Preprints and papers

Notes and seminar slides

• Deformation quantisation for (-2)-shifted symplectic structures
(arXiv:1809.11028)

• A differential graded model for derived analytic geometry
(arXiv:1805.08538)

• Quantisation of derived Poisson structures
(arXiv:1708.00496)

• Non-abelian reciprocity laws and higher Brauer--Manin obstructions
(arXiv:1704.03021)
Also see older slides below.

• On q-de Rham cohomology via Lambda-rings
(arXiv:1608.07142)
Also see slides below.

• Quantisation of derived Lagrangians
(arXiv:1607.01000)
Also see GAP slides 3 below.

• Deformation quantisation for unshifted symplectic structures on derived Artin stacks
(arXiv:1604.04458), Selecta Math. (N.S.) 24(4), 3027--3059, 2018. doi:10.1007/s00029-018-0414-2.
Also see GAP slides 3 below.

• Smooth functions on algebraic K-theory
(arXiv:1602.06222)
Also see slides below.

• Deformation quantisation for (-1)-shifted symplectic structures and vanishing cycles
(arXiv:1508.07936)
Also see GAP slides 3 below.

• Shifted symplectic and Poisson structures on derived N-stacks
(arXiv:1504.01940), J. Topol. 10 (1), 178-210, 2017.
Also see slides below.

• A K-theoretic interpretation of real Deligne cohomology
(arXiv:1411.5705), Adv. Math. 320C (2017) 795-826, doi: 10.1016/j.aim.2017.09.018.
Also see older slides below.

• Tannaka duality for enhanced triangulated categories
(arXiv:1309.0637)
Subdivided as follows:
Tannaka duality for enhanced triangulated categories I: reconstruction
Tannaka duality for enhanced triangulated categories II: t-structures and homotopy types

• Analytic non-abelian Hodge theory
(arXiv:1212.3708), Geom. Topol. 21:1, 841-902, 2017, doi:10.2140/gt.2017.21.841.

• Semiregularity as a consequence of Goodwillie's theorem
(arXiv:1208.3111)
Also see slides below.

• Real non-abelian mixed Hodge structures for quasi-projective varieties: formality and splitting
(arXiv:1104.1409), Mem. AMS. 243 (1150) vi+178 pp., 2016.

• Constructing derived moduli stacks
(arXiv:1101.3300), Geom. Topol. 17:3 (2013) 1417-1495. doi:10.2140/gt.2013.17.1417.

• Derived moduli of schemes and sheaves
(arXiv:1011.2742), J. K-Theory 10(1), 41-85, 2012.

• Representability of derived stacks
(arXiv:1011.2189), J. K-Theory 10(2), 413-453, 2012.

• On l-adic pro-algebraic and relative pro-l fundamental groups
in "The Arithmetic of Fundamental Groups PIA 2010", Contributions in Mathematical and Computational Sciences Vol. 2, 245-279, 2012.

• The homotopy theory of strong homotopy algebras and bialgebras
(arXiv:0908.0116), Homology, Homotopy and Applications 12(2), 2010, 39-108.

• Presenting higher stacks as simplicial schemes
(arXiv:0905.4044), Adv. Math. 238 (2013), 184-245; doi:10.1016/j.aim.2013.01.009.
See notes below for an overview.
See this revision for an attempt to bring indices into line with later versions of HAG2.

• Hodge structures on analytic moduli of real pluriharmonic bundles
(arXiv:0902.0766), largely superseded by 1212.3708.

• Derived deformations of Artin stacks
(arXiv:0805.3130), Comm. Anal. Geom. 23(3), 419-477, 2015.

• Galois actions on homotopy groups of algebraic varieties
(arXiv:0712.0928), Geom. Topol. 15:1 (2011), 501-607; doi:10.2140/gt.2011.15.501.

• Derived deformations of schemes
(arXiv:0908.1963), Comm. Anal. Geom. 20(3), 529-563, 2012.

• Unifying derived deformation theories
(arXiv:0705.0344), Adv. Math. 224 (2010), no.3, 772-826, corrigendum 228 (2011), no.4, 2554-2556; doi:10.1016/j.aim.2009.12.009.
The local copy and and arXiv v6 incorporate the changes listed in this corrigendum.
See Rome notes below for an overview.

• Non-abelian real Hodge theory for proper varieties
(math.AG/0611686), superseded by 1104.1409.

• Pro-algebraic homotopy types
(math.AT/0606107), Proc. London Math. Soc. 2008 97: 273-338; doi: 10.1112/plms/pdn004.

• Weight decompositions on etale fundamental groups
(math.AG/0510245), Amer. J. Math. 131 (2009), no. 3, 869-891.

• The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kaehler manifold
(math.CV/0502451), Ann. Fac. Sci. Toulouse Math. (6), 16(1): 147-178, 2007.

• Galois actions on the pro-l-unipotent fundamental group
(math.AG/0404314), largely superseded by 0712.0928.

• The structure of the pro-l-unipotent fundamental group of a smooth variety
(math.AG/0401378), largely superseded by 0510245.

• Deformations of schemes and other bialgebraic structures,
Trans. Amer. Math. Soc. 360 (2008) 1601-1629. (Mostly contained in 0311168.)
Also see slides below.

• Deforming l-adic representations of the fundamental group of a smooth variety,
J. Algebraic Geom., 15 (2006), 415-442. (Mostly contained in the two preprints below.)

• The deformation theory of representations of the fundamental group of a smooth variety
(math.AG/0401344)

• Deformations via simplicial deformation complexes
(math.AG/0311168)

• An outline of shifted Poisson structures and deformation quantisation in derived differential geometry
(arXiv:1804.07622)

• Slides on smooth functions on algebraic K-theory, Imperial 2017.

• Slides on q-de Rham cohomology via Lambda-rings, Bordeaux 2016.

• Slides from a short lecture course on "Derived algebraic geometry with a view to quantisation" 1, 2, 3, GAP XIV, Sheffield 2016.

• Slides on non-abelian reciprocity laws for modular curves, Imperial workshop 2015.

• Slides on shifted symplectic and Poisson structures, Warwick conference 2015, Manchester 2016 (aimed at a more generalist audience).

• Slides on K-theory and Deligne cohomology, Lancaster conference 2015.

• Slides on semiregularity.

• Derived log stacks after Olsson (arXiv:1310.3845), a brief sketch.

• Slides on a concrete approach to higher and derived stacks, AMS Summer Research Institute, Utah 2015.

• Notes characterising higher and derived stacks concretely (arXiv:1105.4853), based on talks given at the i-MATH School on Derived Algebraic Geometry (Salamanca 2009), the GAD I meeting (Montpellier 2010), the British Mathematics Colloquium (Leicester 2011), and a small part of my graduate lecture course in Cambridge.

• Notes from my lecture course "Derived deformation functors", including the comparison between DGLAs and formal moduli problems, given at the Workshop in Deformation Theory II in Rome, are available on Stefano Maggiolo's blog here.

• Derived deformations via bialgebras (a slightly expanded version of my cats3 talk in Pisa 2008).