Context : The dependence of galaxy star formation activity on environment – especially in clusters – at high redshift is still poorly understood , as illustrated by the still limited number of z \gtrsim 1.4 clusters on the one hand , and by the still debated star formation-density relation at high redshift on the other hand .

Aims : The z _ { phot } \sim 2.2 JKCS 041 cluster allows to probe such environmental dependence of star formation activity at an unprecedented combination of redshifts and environments .
Its study permits to enlarge the knowledge of high redshift clusters and to put strong leverage on observational constraints for galaxy evolution models .

Methods : We analyze deep u ^ { * } g ^ { \prime } r ^ { \prime } i ^ { \prime } z ^ { \prime } JHK _ { s } images from the CFHTLS/WIRDS surveys , which cover JKCS 041 cluster field .
We first estimate photometric redshifts based on multi-wavelength photometry .
We then lead a careful analysis to test the presence of a Butcher-Oemler effect .
We work on galaxies within 2 \times r _ { 200 } and with masses \geq 1.34 \times 10 ^ { 11 } M _ { \odot } , and use two comparison clusters at z = 0 and z = 1 of similar mass .
We estimate the radial profiles of the fraction of blue galaxies , taking into account the star aging with decreasing redshift .

Results : After confirming the high redshift nature of JKCS 041 , we find no evidence for a Butcher-Oemler effect between z \sim 2.2 and z \sim 0 for galaxies more massive than 1.34 \times 10 ^ { 11 } M _ { \odot } .
In the cluster center , a change greater than \Delta f _ { blue } / \Delta z = 0.16 between z \sim 0 and z \sim 2.2 would be easily detected .
We also find that JKCS 041 shows a consistent and systematic increase of the fraction of star-forming galaxies with cluster-centric distance , hence with decreasing density , for both a M \geq 1.34 \times 10 ^ { 11 } M _ { \odot } selected sample and a lower mass sample .
In particular , very few ( less than 15 % ) star-forming galaxies are found within r _ { 200 } / 2 among high mass ( M \geq 1.34 \times 10 ^ { 11 } M _ { \odot } ) galaxies .

Conclusions : Our results show that the present-day star formation-density relation is already in place at z \sim 2.2 .