A few states run their own alternative minimum tax alongside the regular state income tax. California's is 7% of alternative income above an exemption that shrinks at higher incomes. The ISO spread counts toward it, just as it does for the federal AMT, so exercising ISOs and holding the shares can trigger a state AMT bill even when nothing was sold. You pay whichever is higher, the regular state tax or the state AMT, and the extra can often be recovered as a credit in later years.
Official IRS source
CA Schedule P (540)
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