A Research Study Looking at the Effect of Semaglutide on the Immune System and Other Biological Processes in People With Alzheimer's Disease

Inclusion Criteria: * Male or female, aged 55-75 years (both inclusive) at the time of signing the informed consent * Mild cognitive impairment (MCI) or mild dementia of the Alzheimer's type according to the National Institute on Aging- Alzheimer's Association (NIA-AA) 2018 criteria * Clinical dementia rating (CDR) global score of 0.5 or 1 at screening (visit 1) * Amyloid positivity established with either historical amyloid positron emission tomography (PET) or historical cerebrospinal fluid (CSF) Aβ1-42 or historical CSF Aβ1-42/Aβ1-40 (historical data within the last 5 years) or blood sample for amyloid biomarker (Aβ42/Aβ40 ratio and p-tau217/np-tau217 ratio) at screening (visit 1) * Treated with acetylcholinesterase inhibitors (approved for the treatment of Alzheimer's disease) and on stable dose for greater than 90 days before screening (visit 1) Exclusion Criteria: * Brain magnetic resonance imaging (MRI) scan suggestive of clinically significant structural central nervous system (CNS) disease confirmed by local read (example cerebral large-vessel disease \[large vessel (cortical) infarcts greater than 10 millimeter (mm) in diameter\], prior macro-haemorrhage \[greater than 1centimeter cube (cm\^3)\], cerebral vascular malformations, cortical hemosiderosis, intracranial aneurism(s), intracranial tumours, changes suggestive of normal pressure hydrocephalus) * Brain MRI scan suggestive of significant small vessel pathology confirmed by local read and defined as greater than 1 lacunar infarct and/or white matter hyperintensity (WMH) Fazekas13 scale greater than 2, (white matter \[WM\] greater than 20 mm) in the deep white matter and periventricular regions * History or evidence of autoimmune diseases such as inflammatory bowel disease, rheumatoid arthritis, lupus, glomerulonephritis, psoriasis (but not limited to): Any other medical condition that would require use of systemic corticosteroids or immunosuppressants or immunostimulants in the 12 months prior to screening (visit 1) * Received a vaccine product (including booster) 4 weeks prior to screening (visit 1) or expected to receive a vaccine product (including booster) before visit 5 * Use of any systemic immunomodulating drugs (small molecules and/or biologics) in the last 12 months prior to screening (visit 1) or anticipated use of such drugs during study intervention period 1 (i.e., during the first 12 weeks of treatment until visit 5), such as corticosteroids for systemic use, immunostimulants and immunosuppressants