Rigid analytic geometry and its applications

By J. Fresnel, M. Put. 2003

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Higher Topos Theory (2006, background): “We will assume in the following discussion that the reader is familiar with the basic ideas of rigid analytic geometry; for an account of this theory we refer the reader to [29].”
Potential Theory and Dynamics on the Berkovich Projective Line (2010, background): “10 of [52]), for each k there are coprime polynomials Pk and Qk, and a unit power series uk ∈ Ak, such that g(z) = (Pk(z)/Qk(z)) ·uk(z) on Vk ∩K.”
Universal Gauss-Thakur sums and $$L$$L-series (2013, background): “This is the standard one-dimensional Tate algebra over C∞ (see [7] for an account of the theory of these algebras).”
A tropical approach to secant dimensions (2006, background): “3(ii) in [17] says that this map is surjective; this is the lifting theorem alluded to before.”
Semistable reduction for overconvergent $F$-isocrystals I: Unipotence and logarithmic extensions (2004, background): “Our reference for notation and terminology in rigid analytic geometry is [7]; see also [18].”
Arithmetic Compactifications of PEL-Type Shimura Varieties (2013, background): “The simpler case of quotients of tori can also be found in [42].”
Néron models, Lie algebras, and reduction of curves of genus one (2004, background): “Using rigid analytic geometry, one can describe the reduction map rK : E(Ks) → E(kalg) as follows (see [14], §5.”