J.P. Pridham

Preprints and papers

Notes, videos and seminar slides

• Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads
(arXiv:2503.05317)

• Non-commutative derived analytic moduli functors
(arXiv:2502.19403)

• Shifted symplectic structures on derived analytic moduli of ell-adic local systems and Galois representations (local copy last updated 29/8/24)
(arXiv:2205.02292)

• Quantization of derived cotangent stacks and gauge theory on directed graphs
(joint with M.Benini and A.Schenkel), Adv. Theor. Math. Phys. Volume 27 (5), 1275-1332, 2023. (arXiv:2201.10225)

• Shifted bisymplectic and double Poisson structures on non-commutative derived prestacks (local copy last updated 26/2/25)
(arXiv:2008.11698)

• Non-commutative derived moduli prestacks,
Adv. Math. Volume 433, 2023, 109300. (arXiv:2008.11684)

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

• A differential graded model for derived analytic geometry
(arXiv:1805.08538), Adv. Math. Volume 360, 22 January 2020, 106922.

• Quantisation of derived Poisson structures (local copy last updated 9/12/24)
(arXiv:1708.00496), to appear in G&T.
Also see slides below.

• Non-abelian reciprocity laws and higher Brauer-Manin obstructions
(arXiv:1704.03021), Algebr. Geom. Topol. 20(2): 699-756 (2020). DOI: 10.2140/agt.2020.20.699
Also see older slides below.

• On q-de Rham cohomology via Lambda-rings
(arXiv:1608.07142), Math. Annalen 375, pages 425–452 (2019), doi:10.1007/s00208-019-01806-7.
Also see older slides below.

• Quantisation of derived Lagrangians (local copy last updated 4/5/25)
(arXiv:1607.01000), Geom. Topol. 26(6) 2405-2489, 2022.
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), Algebr. Geom., 6(6):747–779, 2019.
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 II: t-structures and homotopy types
(arXiv:1309.0637)

• Tannaka duality for enhanced triangulated categories I: reconstruction
(arXiv:1812.10822), J. Noncommut. Geom. 14 (2) 2020, pp. 591–637. DOI: 10.4171/JNCG/374

• 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), Forum of Mathematics, Sigma, 12, p. e126. doi:10.1017/fms.2024.132.
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 local version contains a correction of the completion formula in mixed characteristic.

• 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, and Freiburg videos below for background.

• 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)

• Slides on derived analytic geometry via entire functional calculus and dagger affinoids, Workshop "An invitation to derived geometry", Padua 2024

• Derived deformation functors, Koszul duality, and Maurer-Cartan spaces (a survey with some new material)
(local copy last updated 1/5/25) (math.AG/2503.05307)

• Slides on deformation quantisation of derived Poisson structures, Global Poisson webinar 2023

• Introduction to derived deformation theory, videos from a short lecture course, Freiburg 2022

• An introduction to derived (algebraic) geometry (written jointly with Jon Eugster), Rend. Mat. Appl. (7) 45(1-2), pp.1-109, 2024, expanded notes from a lecture course, Edinburgh 2021
(arXiv:2109.14594)

• Slides on derived Poisson structures, Poisson 2024 conference, Naples (much overlap with those below)
• Slides on shifted Poisson structures, Workshop "Dg-manifolds in Geometry and Physics", IHP Paris 2023 (expanded version, adapted from those below)
• Slides on shifted Poisson structures, part of a Poisson and Lie algebroids minicourse, Edinburgh 2020

• A note on etale atlases for Artin stacks and Lie groupoids, Poisson structures and quantisation, to appear in JGP special issue
(arXiv:1905.09255)

• 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).