… The fourth author was partially supported by NSF grant DMS-2001272. … ered by Bernstein
for complex representations as a consequence of his theorem on finiteness of Hecke algebras. …

… finite and bounded chain complexes of continuous ℓ-adic Galois representations. To go from
one to the other we need to use compactly-supported étale cohomology. Classically, this is …

… his proof of the finiteness of p-adic étale cohomology. Recall … for cohomology with compact
support defined by the syntomic … the ‘undivided’ version of syntomic complexes of sheaves: …

… the tilings by S-adic Rauzy fractals) will help in the quest for a … A more restrictive condition
is the geometric finiteness … that S-adic words with S = {β1,β2,β3} have linear factor complexity […

… of p-adic formal schemes, since it is naturally related to various previously known p-adic
cohomology theories, and thus … We will use the following conventions on the signs of complexes: …

… thick Selmer complex to counter Bellaïche’s secondary p-adic L-… OX -adic leading term formula
for the two-variable p-adic L-… , that the derivative of the secondary p-adic L-function can be …

… To fill this gap, in [34] we introduce and study the a-adic semidualizing complexes; see …
A difference between this result and its predecessors is the presence of support/cosupport …

… The action of CPG,a on the compactly supported l-adic cohomology H … In our p-adic approach
it is not the endoscopic group H that appears naturally but rather its dual group CH. Thus …

… is a complexanalytic space admitting a closed immerson into projective space, then X is the
analytification of a projective complex … Spf Zp (satisfying certain finiteness assumptions), then …

… Hence, the complex quadratic polynomial family features PCF parameters … to the complex
case K = C. Indeed, Rivera-Letelier described similar Misiurewicz bifurcations in the p-adic …