Geodesic
Bigraded invariants for real curves
dos Santos, Pedro F1 ; Lima-Filho, Paulo2
1Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
2Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX 77843, USA
Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 2809-2852
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

For a proper smooth real algebraic curve Σ we compute the ring structure of both its ordinary bigraded Gal(ℂ∕ℝ)–equivariant cohomology [Bull. Amer. Math. Soc. 4 (1981) 208–212] and its integral Deligne cohomology for real varieties [Math. Ann. 350 (2011) 973–1022]. These rings reflect both the equivariant topology and the real algebraic structure of Σ and they are recipients of natural transformations from motivic cohomology. We conjecture that they completely detect the motivic torsion classes.

DOI : 10.2140/agt.2014.14.2809
Classification : 55N91, 14P25
Keywords: equivariant cohomology, Deligne cohomology, real varieties, real curves

dos Santos, Pedro F  1   ; Lima-Filho, Paulo  2

1 Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
2 Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX 77843, USA 
@article{10_2140_agt_2014_14_2809,
     author = {dos Santos, Pedro F and Lima-Filho, Paulo},
     title = {Bigraded invariants for real curves},
     journal = {Algebraic and Geometric Topology},
     pages = {2809--2852},
     year = {2014},
     volume = {14},
     number = {5},
     doi = {10.2140/agt.2014.14.2809},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.2809/}
}
TY  - JOUR
AU  - dos Santos, Pedro F
AU  - Lima-Filho, Paulo
TI  - Bigraded invariants for real curves
JO  - Algebraic and Geometric Topology
PY  - 2014
SP  - 2809
EP  - 2852
VL  - 14
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.2809/
DO  - 10.2140/agt.2014.14.2809
ID  - 10_2140_agt_2014_14_2809
ER  - 
%0 Journal Article
%A dos Santos, Pedro F
%A Lima-Filho, Paulo
%T Bigraded invariants for real curves
%J Algebraic and Geometric Topology
%D 2014
%P 2809-2852
%V 14
%N 5
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.2809/
%R 10.2140/agt.2014.14.2809
%F 10_2140_agt_2014_14_2809
dos Santos, Pedro F; Lima-Filho, Paulo. Bigraded invariants for real curves. Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 2809-2852. doi: 10.2140/agt.2014.14.2809

[1] G E Bredon, Equivariant cohomology theories, Lecture Notes in Math., Springer (1967)

[2] S R Costenoble, S Waner, Equivariant simple Poincaré duality, Michigan Math. J. 40 (1993) 577

[3] D Dugger, Bigraded cohomology of $\mathbb{Z}/2$–equivariant Grassmannians,

[4] H Esnault, E Viehweg, Deligne–Beĭlinson cohomology, from: "Beĭlinson's conjectures on special values of $L$–functions" (editors M Rapoport, N Schappacher, P Schneider), Perspect. Math. 4, Academic Press (1988) 43

[5] B H Gross, J Harris, Real algebraic curves, Ann. Sci. École Norm. Sup. 14 (1981) 157

[6] G Lewis, J P May, J Mcclure, Ordinary $\mathrm{RO}(G)$–graded cohomology, Bull. Amer. Math. Soc. 4 (1981) 208

[7] L G Lewis Jr., The $\mathrm{RO}(G)$–graded equivariant ordinary cohomology of complex projective spaces with linear $\mathbf{Z}/p$ actions, from: "Algebraic topology and transformation groups" (editor T tom Dieck), Lecture Notes in Math. 1361, Springer (1988) 53

[8] C Pedrini, C Weibel, Invariants of real curves, Rend. Sem. Mat. Univ. Politec. Torino 49 (1991) 139

[9] C Pedrini, C Weibel, The higher $K$–theory of real curves, $K$–Theory 27 (2002) 1

[10] P F Dos Santos, P Lima-Filho, Quaternionic algebraic cycles and reality, Trans. Amer. Math. Soc. 356 (2004) 4701

[11] P F Dos Santos, P Lima-Filho, Bigraded equivariant cohomology of real quadrics, Adv. Math. 221 (2009) 1247

[12] P F Dos Santos, P Lima-Filho, Integral Deligne cohomology for real varieties, Math. Ann. 350 (2011) 973

[13] R Silhol, Compactifications of moduli spaces in real algebraic geometry, Invent. Math. 107 (1992) 151

[14] R Silhol, Moduli problems in real algebraic geometry, from: "Real algebraic geometry" (editors M Coste, L Mahé, M F Roy), Lecture Notes in Math. 1524, Springer (1992) 110

Cité par Sources :