The purpose of this study is to see how LY3439539 affects certain proteins found in the spinal fluid of participants with Alzheimer's disease.

Participation in the study will last approximately 9 months with visits about once a month.

Inclusion Criteria:

• Have gradual and progressive change in memory function reported by the participant or informant for 6 months or longer consistent with a diagnosis of dementia due to Alzheimer's disease
• Have a Mini Mental Score Examination score of 16 to 24, inclusive
• Meet plasma pTau criteria, as defined by the sponsor
• Have body mass index within the range of 17 and 32 kilograms per square meter (kg/m²) (inclusive) at screening
• Are women not of childbearing potential and men willing to practice effective contraception throughout the study.
• Have adequate premorbid literacy, vision, and hearing throughout the study duration and able to complete study procedures.
• Have at least 1, and up to 2, study partners who are in frequent contact with the participant (defined as at least 10 hours per week).

Exclusion Criteria:

• Have any contraindications for magnetic resonance imaging (MRI), including claustrophobia or the presence of contraindicated metal (ferromagnetic) implants/cardiac pacemaker.

• Have a screening MRI that shows evidence of significant abnormality.

• Have history of suicidal behavior, or a lifetime history of suicide attempt or acute suicidality.

• Have a history of

  • Severe or ongoing allergy or hypersensitivity reactions
  • Hypersensitivity to immunizations or immunoglobulins
  • Two or more clinically significant or severe drug allergies,
  • Intolerance to topical corticosteroids or severe posttreatment hypersensitivity reactions

• Have current serious or unstable illnesses, including hepatic, renal, gastroenterological, respiratory, cardiovascular, neurologic (other than AD), psychiatric, endocrinologic, immunologic, hematologic disease, or other conditions

• Require treatment with another monoclonal antibody or have received treatment with biologic agents (such as monoclonal antibodies, including marketed drugs) within 3 months or 5 half-lives (whichever is longer) prior to dosing.

• Have criteria that would preclude a lumbar puncture (LP).

• Are currently enrolled in a clinical study involving an investigational product (IP) or any other type of medical research judged not to be scientifically or medically compatible with this study.

• Have a current exposure to amyloid-targeting therapies (ATTs). Prior exposure to ATTs greater than 1 year from the last dose may be permitted at the discretion of the investigator and in consultation with the sponsor.