In his famous book "Selmer complexes", J.Nekovar, speaking about Greenberg conditions, wrote the following sentence (see 0.8.1 p.10)

these are the only local conditions that can be handled by elementary methods; the general case would require a heavy dose of crystalline machinery, which is not yet available

Even though I know all the concepts involved in this sentence, I have absolutely no idea what it means. More precisely

1. What does he mean by “the only local conditions that can be handled by elementary methods" ? EDIT as pointed out in the comments "elementary methods" are methods used in the book but the question is rather why Greenberg's conditions are the only ones to which these methods apply.

2. What was not available in crystalline cohomology at the time he wrote this sentence?

In his famous book "Selmer complexes", J.Nekovar, speaking about Greenberg conditions, wrote the following sentence (see 0.8.1 p.10)

these are the only local conditions that can be handled by elementary methods; the general case would require a heavy dose of crystalline machinery, which is not yet available.

Even though I know all the concepts involved in this sentence, I have absolutely no idea what it means. More precisely

1. What does he mean by “the only local conditions that can be handled by elementary methods" ? EDIT as pointed out in the comments "elementary methods" are methods used in the book but the question is rather why Greenberg's conditions are the only ones to which these methods apply.

2. What was not available in crystalline cohomology at the time he wrote this sentence?

In his famous book "Selmer complexes", J.Nekovar, speaking about Greenberg conditions, wrote the following sentence (see 0.8.1 p.10)

these are the only local conditions that can be handled by elementary methods; the general case would require a heavy dose of crystalline machinery, which is not yet available

Even though I know all the concepts involved in this sentence, I have absolutely no idea what it means. More precisely

1. What does he mean by “the only local conditions that can be handled by elementary methods" ?

2. What was not available in crystalline cohomology at the time he wrote this sentence?

In his famous book "Selmer complexes", J.Nekovar, speaking about Greenberg conditions, wrote the following sentence (see 0.8.1 p.10)

these are the only local conditions that can be handled by elementary methods; the general case would require a heavy dose of crystalline machinery, which is not yet available

Even though I know all the concepts involved in this sentence, I have absolutely no idea what it means. More precisely

1. What does he mean by “the only local conditions that can be handled by elementary methods" ? EDIT as pointed out in the comments "elementary methods" are methods used in the book but the question is rather why Greenberg's conditions are the only ones to which these methods apply.

2. What was not available in crystalline cohomology at the time he wrote this sentence?

In his famous book "Selmer complexes", J.Nekovar, speaking about Greengerg conditions, wrote the following sentence (see 0.8.1 p.10)

these are the only local conditions that can be handled by elementary methods; the general case would require a heavy dose of crystalline machinery, which is not yet available

Even though I know all the concepts involved in this sentence, I have absolutely no idea what it means. More precisely

1. What does he mean by “the only local conditions that can be handled by elementary methods" ?

2. What was not available in crystalline cohomology at the time he wrote this sentence?

In his famous book "Selmer complexes", J.Nekovar, speaking about Greenberg conditions, wrote the following sentence (see 0.8.1 p.10)

these are the only local conditions that can be handled by elementary methods; the general case would require a heavy dose of crystalline machinery, which is not yet available

Even though I know all the concepts involved in this sentence, I have absolutely no idea what it means. More precisely

1. What does he mean by “the only local conditions that can be handled by elementary methods" ?

2. What was not available in crystalline cohomology at the time he wrote this sentence?