Death spikes follow case spikes by about 2 weeks behind because of the incubation period, but, they stay high longer than 2 weeks because once someone who catches the virus -- and is fated to die from it -- they may take anywhere from 2 to 6 weeks for death to finally occur.
Of note in the charts is the percent positive. If it is high (over 5%), then all it takes is for some relaxation of vigilance for community spread to take off again. People think that the virus is beat and so they go to parties (not necessarily the huge parties in the news, but with extended family and friends). With a higher positive rate, there's a good chance someone in that group is positive, and, bam, now ten more are positive.
But if positivity is really low (like around 1%), then even if people let their guard down, there's a good chance no one at the party is infected, and so, no further spread.
But, of course, even with less than 1% positivity, if there's *a lot* of relaxation of control (masks, distance, washing), then eventually, out of a hundred 'parties', one of those parties will become a super spreader, and we're back to a geometric growth in positive cases.
That's why as we "open" we should always rigorously continue to mask-up and distance and wash. Every day should be treated like it was the first day after lock down and you suspect everyone is positive.