feat(RepresentationTheory/Homological/ContCohomology/Sha): define Sha

[Whysoserioushah]

This PR defines the Tate-Shafarevich group in a general setting as intersections of kernels of the natural map between galois cohomology groups.

co-authored-by: @Multramate

---

[github-actions]

PR summary 03332c5cc2

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RepresentationTheory.Homological.ContCohomology.Sha (new file)	2370

---

Declarations diff (regex)

+ mem_tateSha
+ tateSha
+ tateSha_eq_iInf
+ tateSha_eq_ker_pi

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- stale, waiting for the new build)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 96d36ac).

• +5 new declarations
• −0 removed declarations

+ContinuousCohomology.coe_tateSha
+ContinuousCohomology.mem_tateSha
+ContinuousCohomology.tateSha
+ContinuousCohomology.tateSha_eq_iInf
+ContinuousCohomology.tateSha_eq_ker_pi

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
exposed public sections	5062	1

Current commit 03332c5cc2
Reference commit a6e849c904

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.py pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[Multramate]

Is this in the right file? Maybe we can call the file tateSha.

[tb65536]

Can you add a PR description?

[eric-wieser]

Can you add a reference at the end of the docstring?