PET Scan Imaging in Assessing Response in Patients With Esophageal Cancer Receiving Combination Chemotherapy

* Surgically resectable, histologically confirmed esophageal adenocarcinoma, including Siewert gastroesophageal (GE) junction adenocarcinomas types 1 and 2
* T1N1-3M0 or T2-4NanyM0 as determined by endoscopic ultrasound (EUS) and PET/CT (histologic confirmation of lymph involvement is not required); all disease (tumor and nodes) must be both surgically resectable and capable of containment in a radiotherapy field; no T4 tumor with clear evidence of invasion of the vertebral column, heart, great vessels, or tracheobronchial tree
* All patients must have locoregional staging determined by endoscopic ultrasound (EUS) if technically feasible; endoscopy reports or subsequent gastrointestinal (GI) clinic note should clearly state both the T and N stage
* No evidence of distant metastases (as determined by EUS or PET/CT)
* Patients with cervical, supraclavicular, or other nodal disease that is either not included in the radiation field or is not able to be resected at the time of esophagectomy are not eligible
* Patient must have pre-resection tissue available for central pathology review, in case that the patient has a pCR at the time of surgical resection to confirm diagnosis
* Patients must have an fludeoxyglucose F 18 (FDG)-avid tumor with a maximum standard uptake value (SUVmax) of \>= 5.0 on baseline PET/CT scan of primary tumor; baseline PET/CT scan should be performed; if it is necessary to repeat baseline PET/CT scan, reimbursement information is available
* No prior malignancy within 5 years of registration, with the exception of basal or squamous cell skin cancers, or in situ bladder or cervical cancer; patients with prior malignancy treated with surgery only and disease free for more than 5 years are eligible; however, no prior thoracic radiation therapy (RT) or abdominal RT or chemotherapy allowed
* No known contraindication to the use of fluorouracil, taxanes, or platinum compounds
* No history of severe hypersensitivity reaction to Cremophor EL
* Eastern Cooperative Oncology Group (ECOG) performance status 0-1
* Patient must be non-pregnant and non-nursing; women of child bearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 72 hours prior to randomization; women of child-bearing potential include any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy, bilateral tubal ligation or bilateral oophorectomy) or is not postmenopausal (defined as amenorrhea \>= 12 consecutive months; or women on hormone replacement therapy \[HRT\] with documented serum follicle stimulating hormone \[FSH\] level \> 35mIU/mL); even women who are using oral, implanted or injectable contraceptive hormones or mechanical products such as an intrauterine device or barrier methods (diaphragm, condoms, spermicides) to prevent pregnancy or practicing abstinence or where partner is sterile (e.g., vasectomy), should be considered to be of child bearing potential
* Absolute neutrophil count (ANC) \>= 1,500/μL
* Platelet count \>= 100,000/μL
* Bilirubin =\< 1.5 times upper limit of normal (ULN)
* Calculated creatinine clearance \>= 60 mL/min
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 times ULN