**Core Concept**
The patient's presentation of oliguria, peripheral edema, hematuria, proteinuria, and red cell casts with no evidence of an obstructive lesion is suggestive of a glomerulonephritis, specifically one that involves crescent formation. This is a medical emergency that requires prompt diagnosis and treatment to prevent rapid progression to renal failure.

**Why the Correct Answer is Right**
The presence of many glomerular crescents on renal biopsy is a hallmark of rapidly progressive glomerulonephritis (RPGN). RPGN is characterized by the rapid deterioration of kidney function, often leading to end-stage renal disease within weeks to months. The formation of crescents is thought to be due to the proliferation of parietal epithelial cells and the accumulation of monocytes/macrophages, which lead to the obliteration of the Bowman's space. This process is often mediated by the deposition of immune complexes and the activation of the complement system.

**Why Each Wrong Option is Incorrect**
**Option A:** Focal segmental glomerulosclerosis (FSGS) typically presents with nephrotic syndrome, characterized by massive proteinuria and hypoalbuminemia, but it is not usually associated with hematuria or red cell casts. FSGS is also not typically characterized by the presence of glomerular crescents.
**Option B:** Diabetic nephropathy is a common cause of chronic kidney disease, but it typically presents with a more gradual decline in renal function and is not usually associated with hematuria or red cell casts. Diabetic nephropathy is also not typically characterized by the presence of glomerular crescents.
**Option C:** Membranous nephropathy is a cause of nephrotic syndrome, characterized by massive proteinuria and hypoalbuminemia, but it is not usually associated with hematuria or red cell casts. Membranous nephropathy is also not typically characterized by the presence of glomerular crescents.

**Clinical Pearl / High-Yield Fact**
The presence of red cell casts in the urine is a key diagnostic feature of RPGN, as it suggests the presence of glomerulonephritis. Red cell casts are formed when red blood cells are trapped in the tubules of the kidney and are then transported to the urine.

**Correct Answer:** C. Rapidly progressive glomerulonephritis (RPGN).