Volume 15, issue 1 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Galois actions on homotopy groups of algebraic varieties

Jonathan P Pridham

Geometry & Topology 15 (2011) 501–607
Bibliography
1 F Andreatta, A Iovita, Comparison isomorphisms for smooth formal schemes, Preprint (2009)
2 M Artin, B Mazur, Etale homotopy, Lecture Notes in Math. 100, Springer (1969) MR0245577
3 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer (1972) MR0365573
4 P Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. (1971) 5 MR0498551
5 P Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. (1980) 137 MR601520
6 P Deligne, J S Milne, A Ogus, K y Shih, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Math. 900, Springer (1982) MR654325
7 W G Dwyer, D M Kan, Homotopy theory and simplicial groupoids, Nederl. Akad. Wetensch. Indag. Math. 46 (1984) 379 MR770723
8 G Faltings, Crystalline cohomology and $p$–adic Galois representations, from: "Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988)" (editor J I Igusa), Johns Hopkins Univ. Press (1989) 25 MR1463696
9 J M Fontaine, Sur certains types de représentations $p$–adiques du groupe de Galois d'un corps local; construction d'un anneau de Barsotti–Tate, Ann. of Math. $(2)$ 115 (1982) 529 MR657238
10 E M Friedlander, Étale homotopy of simplicial schemes, Annals of Math. Studies 104, Princeton Univ. Press (1982) MR676809
11 P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Math. 174, Birkhäuser Verlag (1999) MR1711612
12 A Grothendieck, Revêtements étales et groupe fondamental (SGA 1), Documents Math. (Paris) 3, Soc. Math. France (2003) MR2017446
13 R M Hain, The Hodge de Rham theory of relative Malcev completion, Ann. Sci. École Norm. Sup. $(4)$ 31 (1998) 47 MR1604294
14 R M Hain, M Matsumoto, Relative pro-$l$ completions of mapping class groups, J. Algebra 321 (2009) 3335 MR2510052
15 V A Hinich, V V Schechtman, On homotopy limit of homotopy algebras, from: "$K$–theory, arithmetic and geometry (Moscow, 1984–1986)" (editor Y I Manin), Lecture Notes in Math. 1289, Springer (1987) 240 MR923138
16 P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monogr. 99, Amer. Math. Soc. (2003) MR1944041
17 G Hochschild, G D Mostow, Pro-affine algebraic groups, Amer. J. Math. 91 (1969) 1127 MR0255690
18 M Hovey, Model categories, Math. Surveys and Monogr. 63, Amer. Math. Soc. (1999) MR1650134
19 D C Isaksen, A model structure on the category of pro-simplicial sets, Trans. Amer. Math. Soc. 353 (2001) 2805 MR1828474
20 U Jannsen, Continuous étale cohomology, Math. Ann. 280 (1988) 207 MR929536
21 N M Katz, $p$–adic properties of modular schemes and modular forms, from: "Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)" (editors W Kuyk, J P Serre), Lecture Notes in Math. 350, Springer (1973) 69 MR0447119
22 L Katzarkov, T Pantev, B Toën, Schematic homotopy types and non-abelian Hodge theory, Compos. Math. 144 (2008) 582 MR2422341
23 L Katzarkov, T Pantev, B Toën, Algebraic and topological aspects of the schematization functor, Compos. Math. 145 (2009) 633 MR2507744
24 K S Kedlaya, Fourier transforms and $p$–adic ‘Weil II’, Compos. Math. 142 (2006) 1426 MR2278753
25 R Kiehl, R Weissauer, Weil conjectures, perverse sheaves and $l$'adic Fourier transform, Ergebnisse der Math. und ihrer Grenzgebiete. 3. Folge. 42, Springer (2001) MR1855066
26 M Kontsevich, Topics in algebra — deformation theory, Lecture notes (1994)
27 L Lafforgue, Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002) 1 MR1875184
28 S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1971) MR0354798
29 A R Magid, On the proalgebraic completion of a finitely generated group, from: "Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001)" (editors S Cleary, R Gilman, A G Myasnikov, V Shpilrain), Contemp. Math. 296, Amer. Math. Soc. (2002) 171 MR1921711
30 J S Milne, Étale cohomology, Princeton Math. Series 33, Princeton Univ. Press (1980) MR559531
31 J W Morgan, The algebraic topology of smooth algebraic varieties, Inst. Hautes Études Sci. Publ. Math. (1978) 137 MR516917
32 M C Olsson, $F$–isocrystals and homotopy types, J. Pure Appl. Algebra 210 (2007) 591 MR2324594
33 M C Olsson, Towards non-abelian $p$–adic Hodge theory in the good reduction case, Mem. Amer. Math. Soc. 210 no. 990, Amer. Math. Soc. (2011)
34 J P Pridham, Formality and splitting of real non-abelian mixed Hodge structures arXiv:0902.0770v2
35 J P Pridham, Galois actions on the pro–$l$–unipotent fundamental group arXiv:math.AG/0404314
36 J P Pridham, Deforming $l$–adic representations of the fundamental group of a smooth variety, J. Algebraic Geom. 15 (2006) 415 MR2219844
37 J P Pridham, Pro-algebraic homotopy types, Proc. Lond. Math. Soc. $(3)$ 97 (2008) 273 MR2439664
38 J P Pridham, Weight decompositions on étale fundamental groups, Amer. J. Math. 131 (2009) 869 MR2530856
39 J P Pridham, The homotopy theory of strong homotopy algebras and bialgebras, Homology, Homotopy Appl. 12 (2010) 39 MR2721031
40 J P Pridham, Unifying derived deformation theories, Adv. Math. 224 (2010) 772 MR2628795
41 J P Pridham, $\ell$–adic pro-algebraic and relative pro–$\ell$ fundamental groups, to appear in “The arithmetic of fundamental groups (PIA 2010)”, (J Stix, editor), Springer, Berlin (2011)
42 G Quick, Profinite homotopy theory, Doc. Math. 13 (2008) 585 MR2466189
43 D Quillen, An application of simplicial profinite groups, Comment. Math. Helv. 44 (1969) 45 MR0242156
44 D Quillen, Rational homotopy theory, Ann. of Math. $(2)$ 90 (1969) 205 MR0258031
45 A Schmidt, Extensions with restricted ramification and duality for arithmetic schemes, Compositio Math. 100 (1996) 233 MR1383466
46 J P Serre, Lie algebras and Lie groups, Lecture Notes in Math. 1500, Springer (1992) MR1176100
47 J P Serre, Cohomologie galoisienne, Lecture Notes in Math. 5, Springer (1994) MR1324577
48 A Shiho, Crystalline fundamental groups and $p$–adic Hodge theory, from: "The arithmetic and geometry of algebraic cycles (Banff, AB, 1998)" (editors B B Gordon, J D Lewis, S Müller-Stach, S Saito, N Yui), CRM Proc. Lecture Notes 24, Amer. Math. Soc. (2000) 381 MR1738868
49 B Toën, Champs affines, Selecta Math. $($N.S.$)$ 12 (2006) 39 MR2244263
50 T Tsuji, Crystalline sheaves, syntomic cohomology and $p$–adic polylogarithms, Caltech seminar notes (2001)
51 V Vologodsky, Hodge structure on the fundamental group and its application to $p$–adic integration, Mosc. Math. J. 3 (2003) 205, 260 MR1996809
52 C A Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Math. 38, Cambridge Univ. Press (1994) MR1269324