Hrushovski, EhudDor, Yuval David2022-03-1820222022-01-262022-03Dor, Yuval David. 2021. Transformal Valued Fields. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.28774952https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37371095By an w-increasing transformal valued field we mean a valued field equipped with a distinguished endomorphism which is locally infinitely contracting on the unit disc. We show that the basic constructions of ramification theory, such as Henselization and strict Henselization, admit meaningful analogues in those generalized settings. Model theoretically, we determine the model companion of the theory of w-increasing transformal valued fields; it is decidable and admits elimination of quantifiers to the level of finite covers. As an application, we determine the elementary theory of algebraically closed valued fields equipped with a distinguished Frobenius, in the regime where the prime power is large.application/pdfenCommutative AlgebraModel TheoryValuation TheoryMathematicsThesis or Dissertation2022-03-180000-0001-8028-766X